Associated to a random experiment two events A and B are such tha… - Vidyadip

Question

Associated to a random experiment two events A and B are such that $\text{P(B)}=\frac{3}{5},\text{P}(\text{A}|\text{B})=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5}$. The value pf P(A) is

$\frac{3}{10}$
$\frac{1}{2}$
$\frac{1}{10}$
$\frac{3}{5}$

✓

Answer

$\frac{1}{2}$

Solution:

$\text{P(B)}=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2},\text{P}(\text{A}\cup\text{B})=\frac{4}{5}$

$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$

$\frac{\text{P}(\text{A}\cap\text{B})}{\text{P(B)}}=\frac{1}{2}$

$\frac{\text{P}(\text{A}\cap\text{B})}{\frac{3}{5}}=\frac{1}{2}$

$\text{P}(\text{A}\cap\text{B})=\frac{3}{10}$

$\text{P(A)}+\text{P(B)}-\text{P}(\text{A}\cup\text{B})=\frac{3}{10}$

$\text{P(A)}+\frac{3}{5}-\frac{4}{5}=\frac{3}{10}$

$\text{P(A)}=\frac{1}{2}$

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