Question

Two different numbers are randomly selected from the set $\{ - 2, -1, 0, 3, 4, 5\}$ and multiplied together. What is the probability that the product is $0?$

$\dfrac{1}{6}$

$\dfrac{1}{5}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

Answer: D

Concepts:basic probability counting pairs

Difficulty rating: 1020

Video solution:

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Written solution:

There are $\binom62=15$ ways to select two different numbers. A product is $0$ exactly when one selected number is $0$ , and there are $5$ choices for the other number. Thus the probability is $\dfrac5{15}=\dfrac13.$

Thus, D is the correct answer.

2016 AMC 8 Problem 13

Answer: D

Difficulty rating: 1020

Video solution:

Written solution:

Problem 13 in Other Years