Answer to Question #151049 in Statistics and Probability for Sakshi Mittal

Question

A man is equally likely to choose any one of the three routes A, B, C from his office,

and his choice of route is not influenced by the weather. If the weather is dry the probabilities

of his being late by routes A, B, C are respectively 1/20, 1/10, 1/8. He sets out on a dry day and reaches his office late. What is the probability that the route chosen was C?

Answer 1

This is a conditional probability case. let P(L) denote the probability of being late and P(C) be the probability of using route C.

$P(C|L)=\frac{P(L\bigcap C)}{P(L)}$

$P(L)=\frac{1}{3}*(\frac{1}{20}+\frac{1}{10}+\frac{1}{8})$

=$\frac {11}{120}$

$P(L\bigcap C)=\frac{1}{3}*\frac{1}{8}$ =$\frac{1}{24}$

$P(C|L)=\frac{1}{24} \div\frac{11}{120}$

=$\frac{5}{11}$