Question

Given P(B | A)=0.75, P(A ∩ B)=0.15, P(B’)=0.7, find P(A ∪ B)

Answer 1

By definition of conditional probability,

P(B | A) = P(A ∩ B) / P(A)

==> P(A) = P(A ∩ B) / P(B | A) = 0.15/0.75 = 0.2

By definition of complement,

P(B') = 1 - P(B)

==> P(B) = 1 - P(B') = 1 - 0.7 = 0.3

Now by the inclusion/exlcusion principle, we have

P(A U B) = P(A) + P(B) - P(A ∩ B)

==> P(A U B) = 0.2 + 0.3 - 0.15 = 0.35