A courier takes the highway, the city road or the hill road with probabilities 1/2, 1/3 and 1/6. A parcel is delayed with probability 1/10 on the highway, 1/5 on the city road and 1/2 on the hill road. A parcel is delayed. What is the probability that it went by the hill road?

Question 109

MediumOriginal question

A courier takes the highway, the city road or the hill road with probabilities $\frac{1}{2}$ , $\frac{1}{3}$ and $\frac{1}{6}$ . A parcel is delayed with probability $\frac{1}{10}$ on the highway, $\frac{1}{5}$ on the city road and $\frac{1}{2}$ on the hill road. A parcel is delayed. What is the probability that it went by the hill road?

\frac{1}{6}

Correct answerYour answer

\frac{1}{5}

Correct answerYour answer

\frac{5}{12}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$P(D) = \frac{1}{2} \times \frac{1}{10} + \frac{1}{3} \times \frac{1}{5} + \frac{1}{6} \times \frac{1}{2} = \frac{3 + 4 + 5}{60} = \frac{1}{5}$ .
The hill road's share: $\frac{1/12}{1/5} = \frac{5}{12}$ .

Worth noting

$\frac{1}{6}$ is the hill road's chance before the delay is known; delays are likeliest there.

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.