A man is known to speak truth 7 out of 10 times. After throwing a die with 100 faces marked 1,2,3,.., 100 on…
A man is known to speak truth 7 out of 10 times. After throwing a die with 100 faces marked 1,2,3,.., 100 on it's faces, the man reports that he got a prime number on the die. What is the probability that it is actually a prime?
$\frac{5}{16}$
$\frac{7}{16}$
$\frac{11}{16}$
$\frac{10}{16}$
Solution
Consider the events
$A=$ Probability that prime number occur
$B=$ Probability that prime number does not occur
$E=$ prime number occur when man reports
25 prime number from 1 to 100
$\therefore \quad P(A)=\frac{25}{100}=\frac{1}{4}$
$P(B)=\frac{75}{100}=\frac{3}{4}$
$P(E / A)=\frac{7}{10}, P(E / B)=\frac{3}{10}$
Required probability
$P(A / E)=\frac{\frac{1}{4} \times \frac{7}{10}}{\frac{1}{4} \times \frac{7}{10}+\frac{3}{4} \times \frac{3}{10}}=\frac{7}{16}$