AMC8 2016

AMC8 2016 · Q13

AMC8 2016 · Q13. It mainly tests Basic counting (rules of product/sum), Probability (basic).

Two different numbers are randomly selected from the set $\{-2, -1, 0, 3, 4, 5\}$ and multiplied together. What is the probability that the product is 0?

从集合$\{-2, -1, 0, 3, 4, 5\}$中随机选取两个不同的数相乘。乘积为0的概率是多少？

(A) $1/6$ $1/6$

(B) $1/5$ $1/5$

(D) $1/3$ $1/3$

(E) $1/2$ $1/2$

Answer

Correct choice: (D)

正确答案：（D）

Solution

There are $6\cdot 5=30$ possible pairs of numbers. For a product to be $0$, either the first factor or the second factor must be $0$, so there are $1\cdot 5+5\cdot 1=10$ such products. The desired probability is $\frac{10}{30}=\frac{1}{3}$.

共有 $6\cdot 5=30$ 种可能的数对。要使乘积为 $0$，要么第一个因数为 $0$，要么第二个因数为 $0$，因此共有 $1\cdot 5+5\cdot 1=10$ 种这样的乘积。所求概率为 $\frac{10}{30}=\frac{1}{3}$。

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