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In an experiment, the probability that event B occurs is -, and the probability that event A occurs given 7 기 7 that event B occurs is - 8 What is the probability that events A and B both occur? Simplify any fractions.

Answer :

ANSWER

P(A and B) = 1/2

EXPLANATION

By the Bayes Theorem we have a relationship between the given probabilities:

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

In this problem P(B) = 4/7 and P(A|B) = 7/8:

[tex]P(A\text{ and B)}=\frac{4}{7}\times\frac{7}{8}=\frac{4}{8}=\frac{1}{2}[/tex]

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