Track / Stage 1 / 226 of 240 #226 of 2444

Problem 226

Combinatorics Difficulty 1.7 Multiple choice CEMC Cayley · Canada · 2014

Two different numbers are randomly selected from the set $\{-3,-1,0,2,4\}$ and then multiplied together. What is the probability that the product of the two numbers chosen is 0?

Pick one

Official solution

There are ten possible pairs of numbers that can be chosen: $-3$ and $-1$ ; $-3$ and $0$ ; $-3$ and $2$ ; $-3$ and $4$ ; $-1$ and $0$ ; $-1$ and $2$ ; $-1$ and $4$ ; $0$ and $2$ ; $0$ and $4$ ; $2$ and $4$ . Each pair is equally likely to be chosen.

Pairs that include 0 (4 pairs) have a product of 0; pairs that do not include 0 (6 of them) do not have a product of 0.

Therefore, the probability that a randomly chosen pair has a product of 0 is $\frac{4}{10}$ or $\frac{2}{5}$ .

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