Probability that A speaks truth is $\frac{4}{5}$. A coin is tossed. A reports that a head appears. The probability that actually there was head is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{4}{5}$
A speaks truth
$P(A)=\frac{4}{5},P(\overline A)=\frac{1}{5}$
H → Head appears
$P(H|A)=\frac{1}{2},P(H|\overline A)=\frac{1}{2}$
So $P(A|H)=\frac{P(A).P(H|A)}{P(A)P(H|A)+P(\bar A)P(H|A)}$
$=\frac{4}{5}$