Download Lesson 14.8 Compound Events

Warm-up
State if the events are independent or dependant and find each probability.
1)
You roll a number cube once. Then roll it again. What
is the probability that you get 2 on the first roll and a
number greater than 4 on the second roll?
Independent. P(2)=1/6 P(greater than 4)= 2/6 P(2,then greater than 4) = 1/18
2)
You toss a coin 3 times. What is the probability you
get 3 tails? Independent. P(T,T,T) = ½ x ½ x ½ = 1/8
3) You have 7 cards. Each card has a letter on it spelling
out the word ALGEBRA. Without replacing a card,
what is the probability of selecting:
a) A, then G
b) E, then A, then R
Dependant. P(A, then G) = 2/7 x 1/6 = 1/21
Dependant. P(E,then A, then R)= 1/7 x 2/6 x 1/5 =1/105
14.8a Compound Events
• The probability of two events occurring is
Compound Events
called a ________________.
Independent and dependent events are
compound events.
Two other types of events are also
Mutually Exclusive
compound events…________________,
Overlapping Events
and ______________________.
Mutually exclusive means they can not happen at the same time!
Overlapping means they can happen at the same time! (You have
to take out the duplicates)
Review…..
• Two events are INDEPENDENT if the
occurrence of one event does not affect
the occurrence of the other! (Replacement
might be a hint)
• Two events are DEPENDENT if the
occurrence of one event does affect the
occurrence of the other. (Nonreplacement)
Disjoint or Mutually exclusive
Events!
Two event are mutually exclusive if they have no outcomes in common.
……..
….
Key Concept: If A and B are mutually exclusive events,
then the probability of A or B is: P(A or B)= P(A) +P(B)
Look for the word “ or “ It means addition
Mutually Exclusive
Ex. 1 A card is randomly selected from a standard deck
of 52 cards. What is the probability that it is a 10 or a
face card?
Disjoint event
Event A= 10
Event B= Face Card
P(A or B) = P(A) + P(B)
P(A or B) =
4 12 16 4



52 52 52 13
Overlapping or Inclusive Event
Ex. 2 A card is randomly selected from a standard deck of 52
cards. What is the probability that it is a face card or a spade?
Event A=Face Card
Event B= Spade
P(A or B) = P(A)+P(B)-P(A and B)
12 13 3 22 11
 


52 52 52 52 26
As you can see from
the Venn Diagram,
being a spade and a
face card at the same
time is possible.
Your turn to practice
• Ex. 3 What is the probability of rolling a standard six-sided
number cube and getting a 3 or a 5.
P(3) = 1/6
P(5)= 1/6
P(3 or 5)= 1/6 + 1/6 = 1/3
• Ex. 4 You roll a number cube. What is the probability that you
get an odd number or a number greater than 3?
Solution: find the probability of the events. Let event A be getting an
odd number and let Event B be getting number greater than 3.
P(A)=3/6
P(B)= 3/6 P(A and B) = 1/6
P(A or B) = 3/6 + 3/6 – 1/6 = 5/6 0.83
Summary
Name two examples of compound events and
if they would be independent, dependant,
mutually exclusive, or overlapping?
Homework time
• Worksheet 14.8 ALL….make sure you
have the right type of compound event: Is
it Independent?
Dependent?
Mutually Exclusive? Overlapping?
• IT makes a difference: the word and
means: Multiply. The word or means add