AMC8 1991

AMC8 1991 · Q22

AMC8 1991 · Q22. It mainly tests Probability (basic), Parity (odd/even).

Each spinner is divided into 3 equal parts. The results obtained from spinning the two spinners are multiplied. What is the probability that this product is an even number?

每个转盘分为3等份。旋转两个转盘得到的结果相乘。这个积是偶数的概率是多少？

(A) 1/3 1/3

(B) 1/2 1/2

(D) 7/9 7/9

(E) 1 1

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The only way to get an odd number for the product of two numbers is to multiply an odd number times an odd number. This happens if one spins 1 or 3 on the first spinner (2 chances out of 3) and 5 on the second spinner (1 chance out of 3). Thus, the probability of an odd product is $\frac{2}{3}\times\frac{1}{3}=\frac{2}{9}$. If one does not get an odd product, then the product is even. Hence the probability of an even product is $1-\frac{2}{9}=\frac{7}{9}$.

答案（D）：要使两个数的乘积为奇数，唯一的方法是用奇数乘奇数。若第一个转盘转到 1 或 3（3 种结果中有 2 种），且第二个转盘转到 5（3 种结果中有 1 种），就会发生这种情况。因此，乘积为奇数的概率是 $\frac{2}{3}\times\frac{1}{3}=\frac{2}{9}$。如果没有得到奇数乘积，那么乘积就是偶数。所以乘积为偶数的概率是 $1-\frac{2}{9}=\frac{7}{9}$。

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