Question

Abe holds $1$ green and $1$ red jelly bean in his hand. Bea holds $1$ green, $1$ yellow, and $2$ red jelly beans in her hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{3}{8}$

$\frac{1}{2}$

$\dfrac{2}{3}$

Video solution:

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Written solution:

There are $2\cdot4=8$ equally likely ways for Abe and Bea to choose their jelly beans. The colors match if they both choose green, which can happen in $1$ way, or if they both choose red, which can happen in $1\cdot2=2$ ways.

Thus $3$ of the $8$ outcomes match, for probability $\dfrac{3}{8}$ .

Thus, C is the correct answer.

2013 AMC 8 Problem 14

Video solution:

Written solution:

Problem 14 in Other Years