P(A cup B) = P(A cap B) if and only if relation between P(A) and P(B) is

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14.Probability

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$P(A \cup B) = P(A \cap B)$ if and only if the relation between $P(A)$ and $P(B)$ is

A

$P(A) = P(\bar A)$

B

$P\,(A \cap B) = P(A' \cap B')$

C

$P\,(A) = P\,(B)$

D

None of these

(IIT-1985)

Solution

(c) $P(A) = P(B)$

As this gives $P(A \cup B) = P(A) + P(B) – P(A \cap B)$

or $P(A) = 2P(A) – P(A)$$ \Rightarrow P(A \cup B) = P(A \cap B).$

Standard 11

Mathematics

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