AMC8 2004

AMC8 2004 · Q21

AMC8 2004 · Q21. It mainly tests Probability (basic), Parity (odd/even).

Spinners A and B are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?

转盘 A 和 B 同时旋转。每个转盘上的箭头等可能地落在每个数字上。两个转盘数字的乘积为偶数的概率是多少？

(A) \frac{1}{4} \frac{1}{4}

(B) \frac{1}{3} \frac{1}{3}

(D) \frac{2}{3} \frac{2}{3}

(E) \frac{3}{4} \frac{3}{4}

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) In eight of the twelve outcomes the product is even: $1\times 2,\ 2\times 1,\ 2\times 2,\ 2\times 3,\ 3\times 2,\ 4\times 1,\ 4\times 2,\ 4\times 3.$ In four of the twelve, the product is odd: $1\times 1,\ 1\times 3,\ 3\times 1,\ 3\times 3.$ So the probability that the product is even is $\frac{8}{12}$ or $\frac{2}{3}.$

（D）在十二种结果中，有八种结果的乘积是偶数：$1\times 2,\ 2\times 1,\ 2\times 2,\ 2\times 3,\ 3\times 2,\ 4\times 1,\ 4\times 2,\ 4\times 3.$ 在十二种结果中，有四种结果的乘积是奇数：$1\times 1,\ 1\times 3,\ 3\times 1,\ 3\times 3.$ 因此乘积为偶数的概率是 $\frac{8}{12}$ 或 $\frac{2}{3}.$

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