AMC10 2016 B

AMC10 2016 B · Q12

AMC10 2016 B · Q12. It mainly tests Probability (basic), Parity (odd/even).

Two different numbers are selected at random from $\{1,2,3,4,5\}$ and multiplied together. What is the probability that the product is even?

从 $\{1,2,3,4,5\}$ 中随机选取两个不同的数并将它们相乘。乘积为偶数的概率是多少？

(A) 0.2 0.2

(B) 0.4 0.4

(D) 0.7 0.7

(E) 0.8 0.8

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The product of two integers is odd if and only if both integers are odd. Thus the probability that the product is odd is $\frac{3}{5}\cdot\frac{2}{4}=0.3$, and the probability that the product is even is $1-0.3=0.7$.

答案（D）：两个整数的乘积为奇数当且仅当这两个整数都是奇数。因此，乘积为奇数的概率是 $\frac{3}{5}\cdot\frac{2}{4}=0.3$，而乘积为偶数的概率是 $1-0.3=0.7$。

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