- Home
- Standard 11
- Mathematics
14.Probability
easy
આપેલ ઘટનાઓ $A$ અને $B$ માટે $P(A)=\frac{1}{2}, P(A \cup B)=\frac{3}{5}$ અને $\mathrm{P}(\mathrm{B})=p .$ આપેલ છે. જો ઘટનાઓ નિરપેક્ષ હોય તો $p$ માં શોધો.
A
$\frac{1}{5}$
B
$\frac{1}{5}$
C
$\frac{1}{5}$
D
$\frac{1}{5}$
Solution
When $A$ and $B$ are independent, $P(A \cap B)=P(A) P(B)=\frac{1}{2} p$
It is known that, $P(A \cup B)=P(A)+P(B)-P(A \cap B)$ $\Rightarrow \frac{3}{5}=\frac{1}{2}+p-\frac{1}{2} p$
$\Rightarrow \frac{3}{5}=\frac{1}{2}+\frac{p}{2}$
$\Rightarrow \frac{p}{2}=\frac{3}{5}-\frac{1}{2}=\frac{1}{10}$
$\Rightarrow p=\frac{2}{10}=\frac{1}{5}$
Standard 11
Mathematics
