ProbabilityHard

Question

For any two events A & B defined on a sample space,

Options

A.P(A/B) ≥ , P (B) ≠ 0 is always true

B.P = P(A) - P(A ∩ B)

C.P(A ∪ B) = 1 - P (A^c). P (B^c), if A & B are independent

D.P(A ∪ B) = 1 - P (A^c). P (B^c), if A & B are disjoint

Solution

(A) P(A/B) =

(B) P(A ∪ B) = P(A) + P(B) - P(A) P(B)
A & B are ind.
= P(A) (1 - P(B) + P(B)
= P(A) + P(B) + 1 - 1
= P(A) - + 1
⇒ 1 + (P(A) - 1) = 1 -

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