In: Math
Let A and B be two subsets of the sample space of an experiment. If P(A) = 0.35, P(B) = 0.55, and P(A ∩ B) = 0.1, find (i) p(A ∩ Bc) (ii) p(A U B)c (iii) p(A ∩ B)c (iv) p(Ac ∩ Bc)
Solution :
Given that,
P(A) = 0.35
P(B) = 0.55
P(A B) = 0.1
(i) P(A B c) = P(A) - P(A B) = 0.35 - 0.1 = 0.25
(ii) P(A B)c = 1 - P(A B)
P(A B) = = P(A ) + P(B) - P(A B) = 0.35 + 0.55 - 0.1 = 0.8
P(A B)c = 1 - P(A B) = 1 - 0.8 = 0.2
(iii) P(A B)c = 1 - P(A B) = 1 - 0.1 = 0.9
(iv)
P(Ac B c) = P(A B)c = 1 - P(A B) = 1 - 0.8 = 0.2