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?

$\frac13$

$\frac49$

$\frac12$

$\frac59$

$\frac{11}{18}$

答案：D

知识点：probability 奇偶性

难度评级：1330

小提示：

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

大提示：

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

解答：

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.

1997 AMC 12 第 10 题

答案：D

难度评级：1330

小提示：

大提示：

解答：

其他年份的第 10 题