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14.Probability
normal
$P(A \cup B) = P(A \cap B)$ 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
Similar Questions
Fill in the blanks in following table :
$P(A)$ | $P(B)$ | $P(A \cap B)$ | $P (A \cup B)$ |
$0.35$ | ……….. | $0.25$ | $0.6$ |
easy