14.Probability
medium

જો $A$ અને $B$ બે ઘટનાઓ છે કે જેથી  $P\,(A \cup B) = P\,(A \cap B),$ તો સાચો સંબંધ મેળવો.

A

$P\,(A) + P\,(B) = 0$

B

$P\,(A) + P\,(B) = P\,(A)\,P\,\left( {\frac{B}{A}} \right)$

C

$P\,(A) + P\,(B) = 2\,P\,(A)\,P\,\left( {\frac{B}{A}} \right)$

D

એકપણ નહીં.

(IIT-1998)

Solution

(c) $P(A \cup B) = P(A) + P(B) – P(A \cap B)$

$ \Rightarrow P(A \cap B) = P(A) + P(B) – P(A \cap B)$

{$\because (P \cap B ) = P( \cup B) $}

$ \Rightarrow 2P(A \cap B) = P(A) + P(B)$

$ \Rightarrow 2P(A)\,.\,\frac{{P(A \cap B)}}{{P(A)}} = P(A) + P(B)$

$ \Rightarrow 2P(A).P\left( {\frac{B}{A}} \right) = P(A) + P(B)$.

Standard 11
Mathematics

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