Track / Stage 5 / 40 of 400 #640 of 1964

Problem 640

AIME late

Combinatorics Difficulty 5.1 Find the answer

Ivana has two identical dice and on the faces of each are the numbers $-3,-2,-1,0,1,2$ . If she throws her dice and multiplies the results, what is the probability that their product is negative?
A $\frac{1}{4}$
B $\frac{11}{36}$
C $\frac{1}{3}$
D $\frac{13}{36}$
E $\frac{1}{2}$

Your answer

Multiple choice: answer with the letter of the option you want.

Official solution

18. C We can get a negative product if the first die is negative and the second positive, with probability $\frac{3}{6} \times \frac{2}{6}=\frac{6}{36}$ , or if the first die is positive and the second is negative, with probability $\frac{2}{6} \times \frac{3}{6}=\frac{6}{36}$ . Together this gives a probability of $\frac{12}{36}=\frac{1}{3}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.