A, B, C are any three events. If P (S) denotes probability of S happening then P,(A cap (B cup C)) =

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14.Probability

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$A, B, C$ are any three events. If $P (S)$ denotes the probability of $S$ happening then $P\,(A \cap (B \cup C)) = $

A

$P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C)$

B

$P(A) + P(B) + P(C) - P(B)\,P(C)$

C

$P(A \cap B) + P(A \cap C) - P(A \cap B \cap C)$

D

None of these

Solution

(c) $P[A \cap (B \cup C)] = P[(A \cap B) \cup (A \cap C)]$

$ = P(A \cap B) + P(A \cap C) – P[(A \cap B) \cap (A \cap C)]$

$ = P(A \cap B) + P(A \cap C) – P(A \cap B \cap C)$.

Standard 11

Mathematics

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(IIT-1998)