有两个盒子，每个盒子内都有分别标有 1，2，3 的三个筹码。从每个盒子里都随机抽取一个筹码并把上面标的数字相乘，那么乘积是偶数的概率是多少？

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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