Question

Probability that $A$ speaks truth is $\frac{3}{4}$. If a coin is tossed and $A$ reports that a head appears, then the probability that head actually appeared is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{3}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is C $\frac{3}{4}$

Probability that head actually appears $P\left(H\right)=\frac{1}{2}$
Probability that head does not appear $P\left(T\right)=\frac{1}{2}$
Let $E$ be the event that $A$ reports head appears, then
$P\left(H|E\right)=\frac{P\left(E|H\right)P\left(H\right)}{P\left(E|T\right)P\left(T\right)+P\left(E|H\right)P\left(H\right)}$
$=\frac{3}{4}$