P(B'|A)=? and P(A' intersection B), when both events are mutually exclusive

Question

when two events A and B are mutually exclusive, then what is the probability of P(B'|A), P(A'|B). P(A), P(B) and P(A∩B) are given. 

Answer 1

Does the problem actually state that the events are mutually exclusive? If so, this means that P(A∩B)=0, which would mean that P(B|A) and P(A|B) would both equal zero, meaning that P(B'|A) and P(A'|B) would both equal 1, regardless of what the values of P(A) and P(B) are. If the given value for P(A∩B) is not zero, then the two events are not mutually exclusive. If they are not mutually exclusive, you can solve for the probabilities using the method below.

 

First, you need to solve for  P(B|A) and P(A|B). Use the formula P(B|A)= P(B∩A)/P(A).

 

Then, you can find P(B'|A) and P(A'|B) using the complement rule for conditional probability: P(B'|A)= 1- P(B|A)

 

I hope this helps.

 

Samantha B.