Download Dependent Events

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Notes: Dependent Events
Statistics and Probability
Probability: Probability theory is the branch of mathematics that studies chance.
What Are Dependent Events?
What happens if two socks are blindly taken without replacement from a drawer with four
orange stocks and two blue stocks?
The probability P (A) that the first sock is blue is ………………..
The probability P (B) that the second sock is blue is ……………..This depends on whether the
first one taken was blue or orange. If the first one taken was blue, then there are four orange
socks and one blue sock left, so the probability that the second is blue is ………. If the first one
taken was orange, then there are three orange and two blue socks left, so the probability that
the second sock is blue is ……….
The value of P (B) depends on the outcome of event A. For this reason, selection without
replacement is considered to be dependent events.
Example:
You randomly choose a marble, put it back, and then randomly choose another marble. Are the
events “choose a red marble first” and “choose a blue marble second” independent or
dependent events?
Definition:
If A and B are dependent events, then P (A  B) = P (A)  P (BIA)
B given A
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Practice:
1. Explain the difference between independent events and dependent events.
2. A drawer has 7 white socks, 5 blue socks and 9 white socks. You randomly choose one
sock out of the drawer, and then randomly choose another one without replacing the
first. What is the probability that both socks are white?
3. Find the probability that both socks are blue if the first one picked is not replaced.
4. Events A and B are dependent events. Find P(A and B)
a. P ( A)  0.9 P( BA)  0.8
b. P ( A)  0.6 P( BA)  0.25
c. P ( A)  0.25 P( BA)  0.2
5. Each integer from 1 through 10is written on a separate piece of paper. You randomly
choose numbers one at a time, but you do not replace them. Find the probability that
both events A and B will occur.
a. Event A: The first number you choose is an odd number
Event B: The second number you choose is an odd number
b. Event A: The first number you choose is a 2.
Event B: the second number you choose is an even number.
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6. The table below shows the size and color of paper clips in a box. You randomly choose
paper clips one at a time from the box, but you do not replace them. What is the
probability that the first three paper clips that you choose are small and yellow?
Small
Large
Red
10
10
Blue
10
10
Yellow
15
15
In problems 7-9, assume that no replacement is made after each selection:
7. A box contains 5 white and 6 red marbles. What is the probability of successfully
drawing, in order, a red marble and then a white marble?
8. A bag contains 3 red, 2 white, and 6 blue marbles. What is the probability of
drawing, in order, 2 red, 1 blue, and 2 white marbles?
9.
Fifteen airmen are in the line crew. They must take care of the coffee mess and line
shack cleanup. They put slips numbered 1 through 15 in a hat and decide that
anyone who draws a number divisible by 5 will be assigned the coffee mess and
anyone who draws a number divisible by 4 will be assigned cleanup. The first
person draws a 4, the second a 3, and the third an 11. What is the probability that
the fourth person to draw will be assigned
a. the coffee mess?
b. the cleanup?
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10. An art class consists of 8 boys and 10 girls. The Arts teacher randomly selects 3
students to present their work. Find the probability that all students selected are girls.
11. A bag contains 20 red marbles and 20 blue marbles. You randomly draw a marble from
the bag, and then you draw another marble. Do you have a greater probability of
drawing 2 red marbles if you replace the first marble after you draw it, or if you do not
replace it? Explain your answer.
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Name:
Notes: Review of Independent and Dependent Events
Statistics and Probability
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2.
Two different dice (red and white) are rolled and the numbers that appear are
recorder. Describe an appropriate sample space (set of possible outcomes).
Hint: There are 36 possible outcomes.
Consider the experiment of rolling two fair dice. Determine whether or not the two
given events A and b are independent or dependent events.
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5.
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