Paper 1 · conditional probability

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

Get the full paper, not just one question

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