Let A and B be two subsets of the sample space of an experiment. If P(A)...

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)

Solutions

Expert Solution

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(A^c B ^c) = P(A B)^c = 1 - P(A B) = 1 - 0.8 = 0.2

milcah answered 9 months ago

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