AMC8 2013

AMC8 2013 · Q8

AMC8 2013 · Q8. It mainly tests Basic counting (rules of product/sum), Probability (basic).

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

公平硬币抛掷 3 次。至少两次连续正面（heads）的概率是多少？

(A) \frac{1}{8} \frac{1}{8}

(B) \frac{1}{4} \frac{1}{4}

(D) \frac{1}{2} \frac{1}{2}

(E) \frac{3}{4} \frac{3}{4}

Answer

Correct choice: (C)

正确答案：（C）

Solution

There are $2^3 = 8$ ways to flip the coins, in order. There are two ways to get exactly two consecutive heads: HHT and THH. There is only one way to get three consecutive heads: HHH. Therefore, the probability of flipping at least two consecutive heads is $\boxed{\textbf{(C)}\frac{3}{8}}$.

抛掷 3 次硬币共有$2^3 = 8$种可能结果，按顺序排列。恰好两次连续正面的有两种方式：HHT 和 THH。三次连续正面的只有一种方式：HHH。因此，至少两次连续正面的概率是$\boxed{\textbf{(C)}\frac{3}{8}}$。

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