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

$\dfrac{5}{16}$

$\dfrac{3}{8}$

$\dfrac{1}{2}$

$\dfrac{5}{8}$

$\dfrac{11}{16}$

答案：E

知识点：二项概率组合

难度评级：1550

小提示：

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.

大提示：

按选择哪些次抛掷为正面来计数。

Count outcomes by choosing which tosses are heads.

解答：

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.

2002 AMC 8 第 21 题

答案：E

难度评级：1550

小提示：

大提示：

解答：

其他年份的第 21 题