1. Tardigrade
  2. Question
  3. Mathematics
  4. Probability that A speaks truth is (4/5).A coin is tossed. A reports that a head appears. The probability that actually there was head is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Solution:

$P\left(E_{1}\right)=P\left(E_{2}\right)=\frac{1}{2} \,\,P\left(B / E_{1}\right)=\frac{4}{5}$
$B: A$ reports head $P\left(B / E_{2}\right)=\frac{1}{5}$
$P\left(E_{1} / B\right)=\frac{\frac{4}{5} \times \frac{1}{2}}{\frac{4}{5} \times \frac{1}{2}+\frac{1}{5} \times \frac{1}{2}}=\frac{4}{5}$