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and 6 In an experiment, the probability that event A occurs is the probability that event B occurs is 9 7 4 the probability that events A and B both occur is - 9 What is the probability that A occurs given that B occurs? Simplify any fractions.

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ANSWER

P(A|B) = 1

EXPLANATION

By the Bayes rule:

[tex]P(A|B)=\frac{P(A\text{ and B)}}{P(B)}[/tex]

In this problem both probabilities are equal: P(A and B) = 4/9 and P(B) = 4/9. The probability of A given B is:

[tex]P(A|B)=\frac{4/9}{4/9}=1[/tex]

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