Question

硬币 $A$ 抛三次，硬币 $B$ 抛四次。两枚公平硬币所得到的正面次数相同的概率是多少？

Coin $A$ is flipped three times and coin $B$ is flipped four times. What is the probability that the number of heads obtained from flipping the two fair coins is the same?

$\dfrac{19}{128}$

$\dfrac{23}{128}$

$\dfrac{1}{4}$

$\dfrac{35}{128}$

$\dfrac{1}{2}$

答案：D

知识点：二项概率分类讨论

难度评级：1470

解答：

两者正面数相同可能为 $0, 1, 2$ 或 $3$ 。硬币 $A$ 的权重为 $1, 3, 3, 1$ ，总数为 $8$ ；硬币 $B$ 的权重为 $1, 4, 6, 4, 1$ ，总数为 $16$ 。

所以概率为 $\begin{aligned} &\dfrac{1\cdot 1 + 3\cdot 4 + 3\cdot 6 + 1\cdot 4}{8 \cdot 16} \\ &= \dfrac{35}{128}. \end{aligned}$

所以正确答案是 D。

The two coins match when both show $0, 1, 2,$ or $3$ heads. Coin $A$ has weights $1, 3, 3, 1$ out of $8$ and coin $B$ has weights $1, 4, 6, 4, 1$ out of $16.$

The probability is $\begin{aligned} &\dfrac{1\cdot 1 + 3\cdot 4 + 3\cdot 6 + 1\cdot 4}{8 \cdot 16} \\ &= \dfrac{35}{128}. \end{aligned}$

Thus, the correct answer is D.

2004 AMC 10A 第 10 题

答案：D

难度评级：1470

解答：

其他年份的第 10 题