2002 AMC 8 第 21 题

Question

Harold 将一枚五美分硬币抛四次。他得到的正面数至少和反面数一样多的概率是

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is

\dfrac{5}{16}

\dfrac{3}{8}

\dfrac{1}{2}

\dfrac{5}{8}

\dfrac{11}{16}

正面数至少和反面数一样多，表示有

2

、

3

或

4

个正面。

At least as many heads as tails means

2,

3,

or

4

heads.

按选择哪些次抛掷为正面来计数。

Count outcomes by choosing which tosses are heads.

四次抛硬币共有

2^4=16

个等可能结果。

正面数至少和反面数一样多，意味着得到

2

、

3

或

4

个正面。这样的结果数为

\begin{aligned} &\binom{4}{2}+\binom{4}{3}+\binom{4}{4} \\ &\quad {}=6+4+1=11 \end{aligned}\text{。}

因此概率为

\dfrac{11}{16}

。

所以正确答案是 E。

There are

2^4=16

equally likely outcomes for four coin tosses.

At least as many heads as tails means getting

2,

3,

or

4

heads. The number of such outcomes is

\begin{aligned} &\binom{4}{2}+\binom{4}{3}+\binom{4}{4} \\ &\quad {}=6+4+1=11. \end{aligned}

Thus the probability is

\dfrac{11}{16}.

Thus, E is the correct answer.

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