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14.Probability
medium
જો $A$ અને $B$ બે સ્વત્રંત ઘટનાઓ છે કે જેથી $P\,(A \cap B') = \frac{3}{{25}}$ અને $P\,(A' \cap B) = \frac{8}{{25}},$ તો $P(A) = $
A
$\frac{1}{5}$
B
$\frac{3}{8}$
C
$\frac{2}{5}$
D
$\frac{4}{5}$
(IIT-2002)
Solution
(a) Since events are independent.
So, $P(A \cap B') = P(A) \times P(B') = \frac{3}{{25}}$
$ \Rightarrow P(A) \times \{ 1 – 2P(B)\} = \frac{3}{{25}}$ …..$(i)$
Similarly, $P(B) \times \{ 1 – P(A)\} = \frac{8}{{25}}$ …..$(ii)$
On solving $(i)$ and $(ii)$, we get $P(A) = \frac{1}{5}$ and $\frac{3}{5}$.
Standard 11
Mathematics
