1997 AMC 12 第 10 题

Question

两枚六面骰子的每个面出现的概率都相同。不过，其中一枚骰子把

4

改成了

3

，另一枚骰子把

3

改成了

4

。掷这两枚骰子时，点数之和为奇数的概率是多少？

Two six-sided dice are fair in the sense that each face is equally likely to turn up. However, one of the dice has the

4

replaced by

3

and the other die has the

3

replaced by

4.

When these dice are rolled, what is the probability that the sum is odd?

\frac13

\frac49

\frac12

\frac59

\frac{11}{18}

要使和为奇数，必须一枚骰子掷出奇数，另一枚掷出偶数

An odd sum requires one odd result and one even result

分别数出每枚改过的骰子上标有奇数的面，重复的数字也要计入

Count odd-labeled faces on each modified die, including repeated labels

第一枚改过的骰子有

4

个奇数面和

2

个偶数面；第二枚有

2

个奇数面和

4

个偶数面。因此所求概率为

(\frac{4}{6})(\frac{4}{6})+(\frac{2}{6})(\frac{2}{6})

=\frac{20}{36}=\frac{5}{9}

。正确答案是 D。

The first modified die has

4

odd faces and

2

even faces; the second has

2

odd and

4

even. Thus the probability is

(\frac{4}{6})(\frac{4}{6})+(\frac{2}{6})(\frac{2}{6})

=\frac{20}{36}=\frac{5}{9}.

The correct answer is D.

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