Question

Let A and B be two events with P(A)=0.5, P(B)=0.4, P(A ∩ B')=0.2. Find P(B'/A U B).

Answer 1

To find :

P(B'/ AUB)

Formula: conditional probability,P(A/B)= P(A and B)/ P(B)

Solution : Using conditional probability formula ,

P(B'/AUB)=P(B' and AUB)/P(AUB)

P(B' and AUB)= P(An B')= 0.2

P(An B)= P(A)-P(AnB')=0.5-0.2=0.3

P(AUB)= P(A)+P(B)=P(A n B)= 0.5+0.4-0.3=0.6

Hence, P(B'/AUB)=0.2/0.6=0.33

attached Venn diagram for reference.