Question

抛两枚公平硬币一次。每出现一个正面，就掷一个公平骰子。骰子点数之和为奇数的概率是多少？（注意，如果没有掷骰子，则和为 $0$ 。）

Two fair coins are to be tossed once. For each head that results, one fair die is to be rolled. What is the probability that the sum of the die rolls is odd? (Note that if no die is rolled, the sum is $0.$ )

$\dfrac{3}{8}$

$\dfrac{1}{2}$

$\dfrac{43}{72}$

$\dfrac{5}{8}$

$\dfrac{2}{3}$

答案：A

知识点：条件概率骰子（概率）奇偶性

难度评级：1490

解答：

只要至少掷一个骰子，由对称性，点数和为奇数的概率为 $\tfrac12$ 。

不掷骰子只在两枚硬币都为反面时发生，概率为 $\tfrac14$ ；此时点数和 $0$ 是偶数。因此所求概率为 $\left(1-\tfrac14\right)\cdot\tfrac12=\tfrac38$ 。

所以正确答案是 A。

Whenever at least one die is rolled, by symmetry the sum is odd with probability $\tfrac12.$

No die is rolled only when both coins are tails, with probability $\tfrac14;$ that sum $0$ is even. So the answer is $\left(1-\tfrac14\right)\cdot\tfrac12=\tfrac38.$

Thus, the correct answer is A.

2008 AMC 10B 第 16 题

答案：A

难度评级：1490

解答：

其他年份的第 16 题