Question

Given P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75,find P(ANB).

Answer 1

P(A∪B) = P(A) + P(B) - P(A∩B)

where P(A) is the probability of A happening

P(B) is the probability of B happening

P(A∪B) is the probability of A or B happening

P(A∩B) is the probability of A and B happening

P(A) = 0.5, P(B) = 0.65 and P(AUB) = 0.75

.75 = .5+ .65 - P(A∩B)

.75 =1.15 - P(A∩B)

.75 - 1.15 = -P(A∩B)

-.4 = -P(A∩B)

.4 =P(A∩B)

P(A∩B) = .4