Question

5 In an experiment, the probability that event B occurs is -, and the probability that event A occurs given 8 5 that event B occurs is – 8 What is the probability that events A and B both occur? Simplify any fractions.

Answer 1

We have

probability of B occurs is 5/8

probability that event A occurs given B occurs is 5/8

We have the next formula, that is the conditional probability formula

`P(A|B)=(P(A\cap B))/(P(B))`

where

P(A|B)= probability of A given B

P(B)= probability of B

P(A∩B)=probability of A and B

so we need to isolate the P(A∩B) in order to obtain the probability that events A and B both occur

`P\mleft(A\cap B\mright)=P(A|B)\cdot P(B)=(5)/(8)\cdot(5)/(8)=(25)/(64)`