2013 AMC 8 第 8 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

8.

一枚公平硬币被抛三次。至少出现两个连续正面的概率是多少?

A fair coin is tossed 3 times. What is the probability of at least two consecutive heads?

18\dfrac{1}{8}

14\dfrac{1}{4}

38\dfrac{3}{8}

12\dfrac{1}{2}

34\dfrac{3}{4}

答案:C
知识点:基本概率系统列举
难度评级:960
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文字解答:

至少有两个连续正面的结果是 HHTHHTTHHTHHHHHHHH。三次公平抛硬币共有 23=82^3=8 个等可能结果,所以概率为 38\dfrac{3}{8}

所以正确答案是 C

The outcomes with at least two consecutive heads are HHTHHT, THHTHH, and HHHHHH. There are 23=82^3=8 equally likely outcomes from three fair coin tosses, so the probability is 38\dfrac{3}{8}.

Thus, C is the correct answer.

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