10.5.notebook
February 27, 2014
10.5
Objective: Examine independent and dependent events (D.4.B)
Independent Events: Two events such that the occurrence of one
has no effect on the occurrence of the other
Probability of Independent Events
If A and B are independent events, then the
probability that both A and B occur is:
P(A a n d B) = P(A) x P(B)
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10.5.notebook
February 27, 2014
Example 1
In a survey at a football game, 50 of 75 male fans and 40 of 50 female fans
said that they favor the new team mascot. If 1 male and 1 female fan are
randomly selected, what is the probability that both favor the new mascot?
Example 2
In a Motocross meet, each heat consists of 8 competitors who are
randomly assigned lanes from 1 to 8. What is the probability that a racer will
draw a lane 8 in the 3 heats in which the racer participates?
Example 3
A spinner is divided into ten equal regions numbered 1 to 10. What is the
probability that 3 consecutive spins result in perfect squares?
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10.5.notebook
February 27, 2014
Dependent Events: Two events such that the occurrence of one affects
the occurrence of the other.
Probability of Dependent Events
If A a n d B are dependent events, then the probability that both
A a nd B occur is:
P (A a n d B) = P(A) x P(B Ι A)
P(B Ι A) is the probability of B will occur given A has occurred
Example 4
You randomly select two cards from a standard deck of 52 cards. What is the
probability that the first card is a heart and the second is a club if
a. you replace the first card before selecting the second card.
b. you do not replace the first card?
Try
Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement.
1. not a club, then a club
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10.5.notebook
February 27, 2014
Example 5 Let n be a randomly selected integer from
1 to 20. Find the probability if:
A) n is odd given that it is prime
B) n is 10 given that it is even Example 6
Events A and B are dependent. Find the missing probability.
A) P(A)=.3,P(BΙA)=.6, P(A and B)=_____ B) P(A)=.8, P(BΙA)=_____, P(A and B)=.32
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