Question

Juan rolls a fair regular octahedral die marked with the numbers $1$ through $8.$ Then Amal rolls a fair six-sided die. What is the probability that the product of the two rolls is a multiple of $3?$

$\dfrac{1}{12}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

$\dfrac{7}{12}$

$\dfrac{2}{3}$

Answer: C

Concepts:complementary probability dice (probability)

Difficulty rating: 1430

Solution:

The product is a multiple of $3$ if and only if at least one die shows $3$ or $6.$ The octahedral die avoids $3,6$ with probability $\dfrac68=\dfrac34,$ and the six-sided die avoids them with probability $\dfrac46=\dfrac23.$

So neither shows a multiple of $3$ with probability $\dfrac34\cdot\dfrac23=\dfrac12,$ and the answer is $1-\dfrac12=\dfrac12.$

Thus, the correct answer is C.

2002 AMC 12B Problem 16

Answer: C

Difficulty rating: 1430

Solution:

Problem 16 in Other Years