2016 AMC 10B 第 12 题

Question

从集合

\{1, 2, 3, 4, 5\}

中随机选出两个不同的数并相乘。乘积为偶数的概率是多少？

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?

\ 0.2

\ 0.4

\ 0.5

\ 0.7

\ 0.8

反过来数乘积为奇数的数对。

Count the odd-product pairs instead

总共有

\binom52

对，其中奇数对有

\binom32

对。

There are

\binom32

odd pairs out of

\binom52

pairs

乘积为奇数当且仅当两个数都是奇数。有

\binom 32=3

种奇数对，总共有

\binom 52=10

种数对。因此乘积为奇数的概率为

\frac 3{10} = 0.3

，乘积为偶数的概率为

1-0.3=0.7

。

所以正确答案是 D。

The product is odd if and only if both numbers are odd. There are

\binom 32=3

ways to do this out of a possible

\binom 52=10

ways. This makes the probability of it being odd equal to

\frac 3{10} = 0.3.

This means the probability it is even is

1-0.3=0.7.

Thus, the correct answer is D .

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