Alg II 11­4 Conditional Probability ­ End.notebook
11-4
February 28, 2017
Conditional Probability
Calculators needed!
The probability that an event, B, will occur given that another event, A, has already occurred is called a conditional probability.
You write the conditional probability of event B, given that event A occurs, as P(B|A).
Ex. 1 The table shows students by gender and by type of school in 2005. You pick a student at random to find the following probabilities.
A.
P(female | graduate school)
B.
P(females)
C.
P(four­year | males)
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Alg II 11­4 Conditional Probability ­ End.notebook
February 28, 2017
Ex. 2 Americans recycle increasing amounts through municipal waste collections. The table shows the collection data for 2007. Find the following probabilities.
A. The probability that a sample of recycled waste is paper.
B.
The probability that a sample of recycled waste is plastic.
C.
The probability of recycled plastic.
D.
The probability of plastic waste.
Formula
You can use a formula to find conditional probability.
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Alg II 11­4 Conditional Probability ­ End.notebook
February 28, 2017
Ex. 3 A utility company asked 50 of its customers whether they pay their bills online or by mail. What is the probability that a customer pays the bill online, given that the customer is male?
Probability of Dependent Events
You can rearrange the formula for conditional probability to find the probability of dependent events.
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Alg II 11­4 Conditional Probability ­ End.notebook
February 28, 2017
Ex. 4 A school system compiled the following information from a survey it sent to people who were juniors 10 years earlier. • 85% of the students graduated from high school.
• of the students who graduated, 90% are happy with their present jobs.
• of the students who did not graduate, 60% are happy with their present jobs.
A. What is the probability that a person from the junior class 10 years ago graduated and is happy with his or her present job?
B.
What is the probability that a person from the junior class 10 years ago did not graduate and is happy with his or her present job?
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