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Problem 138

Number theory Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2022

One integer is selected at random from the following list of 15
integers: $1,2,2,3,3,3,4,4,4,4,5,5,5,5,5$ The
probability that the selected integer is equal to $n$ is $\frac{1}{3}$ . What is the value of $n$ ?

Pick one

Official solution

Since the list includes 15 integers, then an integer has a
probability of $\frac{1}{3}$ of being
selected if it occurs $\$\frac{1}{3} \cdot$ 15 =
5$ times in the list.

The integer 5 occurs 5 times in the list and no other integer occurs 5
times, so $n = 5$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.