A student travels to school by bus, car, or on foot with probabilities 1/6, 1/3, and 1/2 respectively. The probability of being late is 1/5 if by bus, 1/4 if by car, and 1/20 if on foot. Given that the student arrives early on a particular day, what is the probability, as a fraction in lowest terms, that the student travelled on foot?

A student travels to school by bus, car, or on foot with probabilities $\frac{1}{6}$ , $\frac{1}{3}$ , and $\frac{1}{2}$ respectively. The probability of being late is $\frac{1}{5}$ if by bus, $\frac{1}{4}$ if by car, and $\frac{1}{20}$ if on foot. Given that the student arrives early on a particular day, what is the probability, as a fraction in lowest terms, that the student travelled on foot?

Model answer

57/103

Explanation

P(foot and early) = (1/2)(19/20) = 19/40. By Bayes' theorem, P(foot | early) = P(foot and early)/P(early) = (19/40)/(103/120) = 57/103.

Derived from ZIMSEC Statistics Paper 1, November 2020, Q1

Danho has every sitting for this paper, with your progress tracked question by question, offline.