Download Topic 11 - Statistics and Probability

Topic 11 - Statistics and Probability
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a
marble at random without looking. Find the probability of each event. Write your answer as a fraction in
simplest form.
____
____
1. P(red)
a.
c.
b.
d.
2. P(blue)
a.
c.
b.
____
d.
3. P(red or white)
a.
c.
b.
____
d.
4. P(blue or purple)
a.
c.
b.
____
d.
5. P(not white)
a.
c.
b.
d.
During lunch at Urbana Middle School today, several students have brought their lunch from home and
several students are ordering a school lunch as shown in the table. Suppose one student is randomly selected
during lunch time. Find the probability of each event. Write as a fraction in simplest form.
Brought lunch from home
Order school lunch
6th Graders
7th Graders
8th Graders
____
6. P(order school lunch)
a.
b.
____
7. P(6th grader)
55
45
32
35
33
c.
d.
____
a.
c.
b.
d.
8. P(not 7th grader)
a.
b.
____
c.
d.
9. P(brought lunch from home or ordered school lunch)
a.
c.
b.
____ 10. P(7th grader or 8th grader)
a.
b.
d. 1
c.
d.
For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
____ 11. tossing a nickel and tossing a quarter
a. 2
c. 6
b. 4
d. 8
____ 12. picking a number from 1 to 4 and choosing the color red, green, or yellow
a. 6
c. 12
b. 9
d. 24
____ 13. choosing a blue, white, or green shirt with khaki or denim pants
a. 6
c. 12
b. 3
d. 10
____ 14. choosing either turkey or ham on wheat or rye bread
a. 2
c. 4
b. 8
d. 12
____ 15. rolling a number cube and choosing a card between the cards marked X and Y
a. 6
c. 8
b. 20
d. 12
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
____ 16. rolling a number cube and tossing a nickel
a. 6
c. 24
b. 8
d. 12
____ 17. choosing a number from 1 to 15 and a vowel from the word COUNTING
a. 120
c. 90
b. 45
d. 55
____ 18. choosing a car with an exterior color of black, red, green, gray, or tan; and choosing a leather or fabric interior
a. 10
c. 15
b. 20
d. 8
____ 19. choosing a tuna, turkey, or cheese sandwich; on wheat or white bread; with a side of potato chips, corn chips,
or baked potato
a. 18
c. 8
b. 24
d. 9
____ 20. choosing a card from a deck of cards numbered 10, 11, 12, ..., 25 and picking a day of the week
a. 175
c. 112
b. 124
d. 156
Glenn surveyed 40 of his classmates to determine their favorite cafeteria food. The results of his survey are
shown in the table.
Favorite
Food
Meatloaf
Tacos
Hamburgers
Pizza
Fish
Number of
Students
4
5
9
18
4
____ 21. What is the probability of meatloaf being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 22. What is the probability of pizza being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 23. What is the probability of tacos being a student’s favorite cafeteria food?
a.
c.
b.
d.
____ 24. Suppose there are 200 students in the cafeteria during lunch. How many students would you expect to choose
hamburgers as their favorite cafeteria food?
a. 50
c. 45
b. 9
d. 36
____ 25. Suppose there are 200 students in the cafeteria during lunch. How many students would you expect to choose
pizza as their favorite cafeteria food?
a. 90
c. 18
b. 104
d. 72
A standard deck of playing cards contains 52 cards. The deck is divided into 4 suits of 13 cards each: hearts,
diamonds, clubs, and spades. Hearts and diamonds are red suits, and clubs and spades are black suits.
Suppose a card is drawn from the deck and recorded. Then the card is reinserted into the deck, the deck is
shuffled, and a second card is drawn and recorded. Find each probability.
____ 26. P(2 spades)
a.
c.
b.
d.
____ 27. P(2 red cards)
a.
c.
b.
d.
____ 28. P(red card on the first draw, club on the second draw)
a.
c.
b.
d.
____ 29. P(Jack on the first draw, heart on the second draw)
a.
c.
b.
d.
____ 30. P(black Ace on the first draw, red King on the second draw)
a.
c.
b.
d.
Short Answer
A deck of 24 cards is numbered 1, 2, 3, ... 24. Suppose you pick a card at random without looking. Find the
probability of each event. Write as a fraction in simplest form.
31. P(21)
32. P(10 or 15)
33. P(odd number)
34. P(greater than or equal to 19)
35. P(factor of 9)
The drama club at Fairborn Middle School is putting on a play for parents, teachers, and students. The club
is made up of the students shown in the table. Suppose one student is randomly selected to read an
announcement for the play over the public address system. Find the probability of each event. Write as a
fraction in simplest form.
Boys
Girls
6th Graders
7th Graders
8th Graders
22
18
10
15
15
36. P(boy)
37. P(girl or boy)
38. P(7th grader or 8th grader)
39. P(not 8th grader)
40. P(6th grader or 8th grader)
For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.
41. choosing pepperoni or mushroom pizza on thin crust or regular crust
42. choosing a letter from the word MATH and choosing a letter from the word FUN
43. choosing a silver, black, or red CD player and choosing a rock, country, or rap CD
44. tossing a coin and choosing a consonant from the word ALGEBRA
45. tossing a penny, tossing a dime, and choosing a card between the cards marked A, B, and C
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
46. choosing an outfit from 6 shirts, 4 pants, and 3 jackets
47. choosing a plain, sesame, sourdough, or blueberry bagel, with chives, plain, or vegetable spread
48. picking a day of the week and a date in the month of April
49. choosing a password that consists of one letter and two numbers from 1 to 9
(Note: the digits can be repeated.)
50. choosing a card from a standard deck of 52 playing cards and rolling a number cube
Solve.
51. A green and a white number cube are rolled. What is the probability that a 3 or a 4 is rolled on the green cube
and an even number is rolled on the white cube?
52. A coin is tossed 4 times. What is the probability of heads on the first toss, tails on the second toss, and heads
on the third and fourth tosses?
53. Horatio rolls a red number cube, rolls a blue number cube, and then tosses a quarter. What is the probability
that he rolls an even number on the red cube, an odd number on the blue cube, and the coin lands on heads?
A bag contains 4 green tokens, 2 red tokens, and 4 purple tokens. Lisa drew a token out of the bag, recorded
the result, and then put the token back into the bag. She did this 30 times and recorded the results in a bar
graph. Use this information to answer the following questions.
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Green
Red
Purple
54. What is the theoretical probability of drawing a red token?
55. What was the experimental probability of drawing a red token? Discuss any differences between this
probability and the theoretical probability of drawing a red token.
56. What is the theoretical probability of drawing a purple token?
57. What was the experimental probability of drawing a purple token? Discuss any differences between this
probability and the theoretical probability of drawing a purple token.
58. Suppose Lisa repeats the experiment an additional 250 times and records the results. About how many times
would you expect her to draw a green token?
Essay
59. A deli offers sub sandwiches on wheat or rye bread, with a choice of ham, salami, or turkey. The deli also
offers customers a choice of American, Provolone, or Cheddar cheese. Suppose a sandwich is chosen at
random.
a. Make a tree diagram that shows all of the possible outcomes.
b. What is the probability that a randomly selected sandwich will be ham on rye with American
cheese?
c. What is the probability that a randomly selected sandwich will contain Provolone cheese or
salami?
60. Maureen baked different kinds of cookies and put them in a cookie jar. The jar contains 4 peanut butter, 6
chocolate chip, 3 oatmeal, and 7 sugar cookies. Assuming the cookies are randomly distributed in the cookie
jar, find each probability.
a.
Suppose Maureen’s brother selects 3 cookies from the jar. What is the probability that
he will select a chocolate chip cookie, then a sugar cookie, and then another chocolate
chip cookie?
b.
Does the situation described in part a represent a set of independent or dependent
events? Explain.
Topic 11 - Statistics and Probability
Answer Section
MULTIPLE CHOICE
1. ANS: D
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Double check your work and try again. /b/ Be sure to write your answer in simplest form. /c/ How
many favorable outcomes are there? How many total outcomes are there? /d/ Correct!
2. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Double check your work and try again. /b/ Correct! /c/ Be sure to write your answer in simplest
form. /d/ How many favorable outcomes are there? How many total outcomes are there?
3. ANS: A
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Correct! /b/ Double check your work and try again. /c/ Be sure to write your answer in simplest
form. /d/ How many favorable outcomes are there? How many total outcomes are there?
4. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Double check your work and try again. /b/ Correct! /c/ How many favorable outcomes are there?
How many total outcomes are there? /d/ Be sure to write your answer in simplest form.
5. ANS: C
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ This is the probability of drawing a white marble. What is the probability that a white marble is not
drawn? /b/ Double check your work and try again. /c/ Correct! /d/ How many marbles are not white? Compare
this number with the total number of possible outcomes.
6. ANS: A
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Correct! /b/ How many students are ordering a school lunch? How many total students are there? /c/
Double check your work and try again. /d/ How many students are ordering a school lunch?
7. ANS: C
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Be careful when simplifying the fraction. Try again. /b/ How many 6th graders are there? /c/
Correct! /d/ Double check your work and try again.
8. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ Double check your work and try again. /b/ Correct! /c/ Be careful when simplifying your fraction.
Try again. /d/ This is the probability that the student is a 7th grader. What is the probability that the student is
not a 7th grader?
9. ANS: D
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF:
STO:
KEY:
NOT:
Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
NY S.C
TOP: Find the probability of a real-world simple event.
Probability, Simple event
MSC: 1999 Lesson 4-8
/a/ How many of the students at Urbana either brought their lunch from home or are ordering a school
lunch? /b/ How many of the students at Urbana either brought their lunch from home or are ordering a school
lunch? /c/ Make sure your answer seems reasonable. Try again. /d/ Correct!
10. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
NOT: /a/ How many students are either a 7th grader or an 8th grader? /b/ Correct! /c/ Double check your
work and try again. /d/ Be careful when simplifying your fraction. Try again.
11. ANS: B
There are four possible outcomes: HH, HT, TH, and TT.
DIF: Basic
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
NOT: /a/ List all of the possible outcomes for the first coin. Then list all of the possibilities for the second
coin, given the result of the first coin. /b/ Correct! /c/ List all of the possible outcomes to make sure they are
all unique. /d/ Double check your work and try again.
12. ANS: C
There are twelve possible outcomes: 1R, 1G, 1Y, 2R, 2G, 2Y, 3R, 3G, 3Y, 4R, 4G, and 4Y.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
NOT: /a/ List all of the possible outcomes for the number. Then branch off each number to list all of the
possible outcomes for the color. /b/ Double check your work and try again. /c/ Correct! /d/ List all of the
possible outcomes to make sure they are all unique.
13. ANS: A
There are six possible outcomes: BK, BD, WK, WD, GK, and GD.
DIF: Basic
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
NOT: /a/ Correct! /b/ List all of the possible shirt outcomes. Then branch off to list all of the possible pant
outcomes, given each shirt outcome. /c/ List all of the possible outcomes to make sure they are all unique. /d/
Double check your work and try again.
14. ANS: C
There are four possible outcomes: turkey on wheat, turkey on rye, ham on wheat, and ham on rye.
DIF: Basic
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
NOT: /a/ List all of the possible outcomes for the type of meat. Then branch off to list all of the possible
outcomes for the type of bread. /b/ List all of the possible outcomes to make sure they are all unique. /c/
Correct! /d/ Double check your work and try again.
15. ANS: D
There are twelve possible outcomes: 1X, 1Y, 2X, 2Y, 3X, 3Y, 4X, 4Y, 5X, 5Y, 6X, and 6Y.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
NOT: /a/ Double check your work and try again. /b/ List all of the possible outcomes to make sure they are
all unique. /c/ List all of the possible outcomes for the number cube. Then branch off to list all of the
outcomes for choosing the card. /d/ Correct!
16. ANS: D
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
6(2) = 12
DIF: Basic
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
NOT: /a/ Multiply the number of outcomes for each event to find the total number of outcomes in the sample
space. /b/ Double check your work and try again. /c/ How many ways can you roll a number cube? How many
ways can you toss a nickel? /d/ Correct!
17. ANS: B
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
15(3) = 45
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
NOT: /a/ How many vowels are there in the word COUNTING? /b/ Correct! /c/ Double check your work and
try again. /d/ Multiply the number of outcomes for each event to find the total number of outcomes in the
sample space.
18. ANS: A
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
5(2) = 10
DIF: Basic
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
NOT: /a/ Correct! /b/ Multiply the number of outcomes for each event to find the total number of outcomes
in the sample space. /c/ How many interior color choices are there? How many types of interior are there? /d/
Double check your work and try again.
19. ANS: A
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
3(2)(3) = 18
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
NOT: /a/ Correct! /b/ Multiply the number of outcomes for each event to find the total number of outcomes
in the sample space. /c/ How many possible outcomes are there for each of the three choices? /d/ Double
check your work and try again.
20. ANS: C
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
16(7) = 112
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
NOT: /a/ How many numbers are there between 10 and 25? /b/ Double check your work and try again. /c/
Correct! /d/ Multiply the number of outcomes for each event to find the total number of outcomes in the
sample space.
21. ANS: B
Write the number of students who voted for meatloaf over the total number of students surveyed and simplify.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
NOT: /a/ Should you include the number of students who prefer meatloaf in your total? /b/ Correct! /c/ How
many students voted for meatloaf? How many students were surveyed? /d/ Be sure to write your answer in
simplest form.
22. ANS: D
Write the number of students who voted for pizza over the total number of students surveyed and simplify.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
NOT: /a/ Be sure to write your answer in simplest form. /b/ Divide the number of students who voted for
pizza by the total number of students surveyed. /c/ How many students voted for pizza? How many students
were surveyed? /d/ Correct!
23. ANS: A
Write the number of students who voted for pizza over the total number of students surveyed and simplify.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
NOT: /a/ Correct! /b/ Divide the number of students who voted for tacos by the total number of students
surveyed. /c/ How many students voted for tacos? How many students were surveyed? /d/ Double check your
work and try again.
24. ANS: C
Students can set up a proportion to solve the problem. One ratio is the number of students who voted for
hamburgers over the number of students surveyed. The other ratio is the number of students who would
choose hamburgers over the number of students in the cafeteria.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
NOT: /a/ Double check your work and try again. /b/ This is how many students out of 40 chose hamburgers.
How many students out of 200 would you expect to choose hamburgers? /c/ Correct! /d/ Be careful when
solving your proportion. Try again.
25. ANS: A
Students can set up a proportion to solve the problem. One ratio is the number of students who voted for pizza
over the number of students surveyed. The other ratio is the number of students who would choose pizza over
the number of students in the cafeteria.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
NOT: /a/ Correct! /b/ Double check your work and try again. /c/ This is how many students out of 40 chose
pizza. How many students out of 200 would you expect to choose pizza? /d/ Be careful when solving your
proportion. Try again.
26. ANS: D
Since the first card is replaced before drawing the second card, the events are independent. Multiply the
probabilities of each event.
DIF: Basic
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
NOT: /a/ To find the probability of two independent events, multiply the probability of the first event by the
probability of the second event. /b/ This is the probability of drawing one spade. What is the probability of
drawing two spades? /c/ Are the two draws dependent or independent events? /d/ Correct!
27. ANS: B
Since the first card is replaced before drawing the second card, the events are independent. Multiply the
probabilities of each event.
DIF: Basic
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
NOT: /a/ This is the probability of drawing one red card. What is the probability of drawing two red cards?
/b/ Correct! /c/ Are the two draws dependent or independent events? /d/ To find the probability of two
independent events, multiply the probability of the first event by the probability of the second event.
28. ANS: A
Since the first card is replaced before drawing the second card, the events are independent. Multiply the
probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
NOT: /a/ Correct! /b/ Are the two draws dependent or independent events? /c/ Double check your work and
try again. /d/ To find the probability of two independent events, multiply the probability of the first event by
the probability of the second event.
29. ANS: C
Since the first card is replaced before drawing the second card, the events are independent. Multiply the
probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
NOT: /a/ Double check your work and try again. /b/ What is the probability of drawing a Jack? What is the
probability of drawing a heart? /c/ Correct! /d/ To find the probability of two independent events, multiply the
probability of the first event by the probability of the second event.
30. ANS: B
Since the first card is replaced before drawing the second card, the events are independent. Multiply the
probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
NOT: /a/ Double check your work and try again. /b/ Correct! /c/ Are the two draws dependent or independent
events? /d/ To find the probability of two independent events, multiply the probability of the first event by the
probability of the second event.
SHORT ANSWER
31. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
32. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
33. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify. There are
12 odd numbers between 1 and 24.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
34. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify. There are 6
numbers that are greater than or equal to 19 and less than or equal to 24.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
35. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify. There are 3
factors of 9: 1, 3, and 9.
DIF: Average
OBJ: 9-1.1 Find the probability of a simple event.
STO: NY S.C
TOP: Find the probability of a simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
36. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Basic
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
37. ANS:
1
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
38. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
39. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-1.2 Find the probability of a real-world simple event.
STO: NY S.C
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
MSC: 1999 Lesson 4-8
40. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
STO: NY S.C
OBJ: 9-1.2 Find the probability of a real-world simple event.
TOP: Find the probability of a real-world simple event.
KEY: Probability, Simple event
41. ANS:
4
MSC: 1999 Lesson 4-8
Make a tree diagram to list all possible outcomes.
There are four possible outcomes: pepperoni with thin crust, pepperoni with regular crust, mushroom with
thin crust, and mushroom with regular crust.
DIF: Basic
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
42. ANS:
12
Make a tree diagram to list all possible outcomes.
There are twelve possible outcomes: MF, MU, MN, AF, AU, AN, TF, TU, TN, HF, HU, and HN.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
43. ANS:
9
Make a tree diagram to list all possible outcomes.
There are nine possible outcomes: silver, rock; silver, country; silver, rap; black, rock; black, country; black,
rap; red, rock; red, country; red, rap.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
44. ANS:
8
Make a tree diagram to list all possible outcomes.
There are eight possible outcomes: heads, L; heads, G; heads, B; heads, R; tails, L; tails, G; tails, B; tails, R.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
45. ANS:
12
Make a tree diagram to list all possible outcomes.
There are twelve possible outcomes: HHA, HHB, HHC, HTA, HTB, HTC, THA, THB, THC, TTA, TTB, and
TTC.
DIF: Average
OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: NY 6.S.9
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
MSC: 1999 Lesson 13-2
46. ANS:
72 outfits
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
6(4)(3) = 72
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
47. ANS:
12 bagels
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
4(3) = 12
DIF: Basic
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
48. ANS:
210
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
7(30) = 210
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
49. ANS:
2,106
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
26(9)(9) = 2,106
DIF: Average
OBJ: 9-3.1 Use multiplication to count outcomes.
STO: NY 6.S.9
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
MSC: 1999 Lesson 13-3
50. ANS:
312
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
52(6) = 312
DIF: Average
STO: NY 6.S.9
OBJ: 9-3.1 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes.
KEY: Probability, Counting
51. ANS:
MSC: 1999 Lesson 13-3
The two events are independent. Multiply the probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
52. ANS:
Each toss of the coin is an independent event. Multiply the probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
53. ANS:
The three events are independent. Multiply the probabilities of each event.
DIF: Average
OBJ: 9-7.1 Find the probability of independent events.
STO: NY S.C
TOP: Find the probability of independent events.
KEY: Probability, Independent events
MSC: 1999 Lesson 13-4
54. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
55. ANS:
; This is lower than the theoretical probability of drawing a red token, which is . The theoretical
probability of an event and the experimental probability do not always match exactly. If Lisa were to continue
the experiment, you would expect her to draw a red token about 20% of the time. Write the number of times
Lisa drew a red token over the total number of trials and simplify.
Any reasonable answer to the second part of the question should be accepted.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
56. ANS:
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
57. ANS:
; This is higher than the theoretical probability of drawing a purple token, which is . The theoretical
probability of an event and the experimental probability do not always match exactly. If Lisa were to continue
the experiment, you would expect her to draw a purple token about 40% of the time. Write the number of
times Lisa drew a red token over the total number of trials and simplify.
Any reasonable answer to the second part of the question should be accepted.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
58. ANS:
100 times
Set up a proportion to solve the problem. One of the ratios should be the theoretical probability of drawing a
green token, and the other ratio should be the number of green token drawn in 250 trials. Students should
realize that the theoretical probability should be used in the proportion instead of the experimental probability
since it is inherently more accurate.
DIF: Average
OBJ: 9-6.1 Find and compare experimental and theoretical probabilities.
STO: NY S.C
TOP: Find and compare experimental and theoretical probabilities.
KEY: Experimental probability, Theoretical probability
MSC: 1999 Lesson 13-1
ESSAY
59. ANS:
a.
There are 18 possible outcomes: WHA, WHP, WHC, WSA, WSP, WSC, WTA, WTP,
WTC, RHA, RHP, RHC, RSA, RSP, RSC, RTA, RTP, and RTC.
b.
There is only 1 favorable outcome (RHA) out of 18 possible outcomes.
c.
There are 10 outcomes that contain either Provolone cheese or salami (WHP, WSA,
WSP, WSC, WTP, RHP, RSA, RSP, RSC, RTP). Write this over the total number of
outcomes and simplify.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
DIF: Advanced
OBJ: 9-8.1 Solve problems and show solutions.
STO: NY 6.S.11
TOP: Solve problems and show solutions.
KEY: Problem solving, Solutions
60. ANS:
a.
For the first draw, there are 6 chocolate chip cookies out of a possible 20 cookies. For the
second draw, there are 7 sugar cookies out of a possible 19 cookies. And for the third draw,
there are 5 chocolate chip cookies out of a possible 18 cookies. Multiply the probabilities
and simplify.
b.
The situation represents a set of dependent events, because the selection of each cookie
depends on which cookies remain in the jar. If the cookies were replaced after each draw,
then the events would be independent.
Any reasonable answer should be accepted.
Assessment Rubric
Level 3 Superior
*Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory
*Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory
*Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
DIF: Advanced
OBJ: 9-8.1 Solve problems and show solutions.
STO: NY 6.S.11
TOP: Solve problems and show solutions.
KEY: Problem solving, Solutions