Probability

Question

If P(A) = 0.7, P(B) = 0.5, P((A ∪ B)^c) = 0.1, find:
(a) P(A ∩ B)
(b) P(A|B)

Answer 1

P(A ∪ B) = 1 - P[(A ∪ B)^c] = 1 - 0.1 = 0.9

 

(a) Use the Inclusion-Exclusion principle.

 

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 0.7 + 0.5 - 0.9 = 0.3

 

(b) Use the definition of Conditional Probability.

 

P(A|B) = P(A ∩ B) / P(B) = 0.3 / 0.5 = 0.6