If A and B are two events such that $P(B)=\frac{3}{5},P(A|B)=\frac{1}{2}$ and $P(A ∪ B)=\frac{4}{5}$, then P(A) is equal to :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{1}{2}$
$P(A|B)=\frac{P(A∩B)}{P(B)}=\frac{1}{2}$
$⇒P(A∩B)=\frac{1}{2}×\frac{3}{10}=\frac{3}{10}$
$P(A∪B)=P(A)+P(B)-P(A∩B)$
$=\frac{4}{5}=P(A)=\frac{3}{5}-\frac{3}{5}⇒P(A)=\frac{4}{5}-\frac{3}{10}=\frac{1}{2}$