Question

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 1

P(A and B) = 1/2

Step-by-step explanation

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

`P(A\text{ and B)}=P(B)\cdot P(A|B)`

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

`P(A\text{ and B)}=(4)/(7)*(7)/(8)=(4)/(8)=(1)/(2)`