- Home
- Standard 11
- Mathematics
14.Probability
medium
If $A$ and $B$ are two events such that $P\,(A \cup B) = P\,(A \cap B),$ then the true relation is
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
None of these
(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
