Each of two boxes contains three chips numbered 1, 2, and 3. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even?

A. $\frac{1}{9}$

B. $\frac{2}{9}$

C. $\frac{4}{9}$

D. $\frac{1}{2}$

E. $\frac{5}{9}$

1. 2015 AMC 8 官方解析

We can instead calculate the probability that their product is odd, and subtract this from 1. In order to get an odd product, we have to draw an odd number from each box. We have a $\frac{2}{3}$ probability of drawing an odd number from one box, so there is a $\left(\frac{2}{3}\right)^2 = \frac{4}{9}$ probability of having an odd product. Thus, there is a $1 - \frac{4}{9} = \frac{5}{9}$ probability of having an even product.

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