Question

Given P(A)=0.8P(A)=0.8, P(B)=0.62P(B)=0.62 and P(A union B)=0.874P(A∪B)=0.874, find the value of P(A unionB)P(A∩B), rounding to the nearest thousandth, if necessary.

Answer 1

Use the inclusion/exclusion principle:

P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

So

P(A ∩ B) = 0.8 + 0.62 - 0.874 = 0.546