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If A, B, C are any three events in an ex...

If A, B, C are any three events in an experiment then show that
(i) `P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B)) "if P"(B^(C)) gt 0`
(ii) `A sube B rArr P(A//C) le P(B//C) "if P(C)" gt 0`
(iii) If A, B are mutually exclusive, then `P(A//B^(C)) = (P(A))/(1-P(B)) "if P(B)" ne 1`
(iv) If A, B are mutually exclusive and `P(A uu B) ne 0 "then" P(A//A uu B) = (P(A))/(P(A) + P(B))`

Text Solution

Verified by Experts

The correct Answer is:
(i) `P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B))`
(ii) `rArr P(A//C) le P(B//C)`
(iii) `P(A//B^(C)) = (P(A nn B^(C)))/(P(B^(C)))=(P(A))/(1-P(B))`
(iv) `P(A nn B) = 0`
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