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14.Probability
medium

ઘટના ${\text{A, B}}$ છે   $P(A \cup B)\,\, = \,\,\frac{3}{4},\,P(A \cap B)\,\, = \,\,\frac{1}{4},\,P(A')\,\, = \,\,\frac{2}{3}$  તો ${\text{P (A' }} \cap {\text{  B)}} = ......$

A

$5/12$

B

$3/8$

C

$5/8$

D

$1/4$

Solution

$P (A) = 1- P(A') = 1 – 2/3 = 1/3$

હવે$,P (A \cup  B)= P (A) + P (B) – P (A \cap C)$

$\begin{gathered}
  \frac{3}{4} = \frac{1}{3}\, + P\,(B)\, – \frac{1}{4}\,\,\,\therefore \,\,\,\,P(B)\, = \frac{3}{4}\, + \frac{1}{4}\, – \,\frac{1}{3}\, = \frac{2}{3} \hfill \\
  P(A' \cap B)\, = \,P\,(B)\, – P\,(A \cap B)\, = \,\frac{2}{3} – \frac{1}{4} = \frac{5}{{12}} \hfill \\ 
\end{gathered} $

Standard 11
Mathematics

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