Find Pr[A?B] under each of the following conditions:

Question

events A and B of a sample space S, but assume that Pr[A] = 0.35 and Pr[B] = 0.5.

Find Pr[A∪B] under each of the following conditions:

(1) If A ⊂ B, then Pr[A∪B] = .

(2) If A ∩ B = ∅, then Pr[A∪B] = .

(3) If A ∩B′ = ∅, then Pr[A∪B] =

Answer 1

if A is a subset of B, then P(AUB) =.50 x .35 x .5 = .35/4 = .0875

if A and B never overlap, then P(AUB) = 0

if A never overlaps Not B, then P(AUB) = same as when A is a subset of B = .0875