Question

一项民意调查显示，所有选民中有 $70\%$ 认可市长的工作。调查员在三个不同场合各随机选择一名选民。恰好一次选择到认可市长工作的选民的概率是多少？

A poll shows that $70\%$ of all voters approve of the mayor's work. On three separate occasions a pollster selects a voter at random. What is the probability that on exactly one of these three occasions the voter approves of the mayor's work?

$0.063$

$0.189$

$0.233$

$0.333$

$0.441$

答案：B

知识点：二项概率独立事件

难度评级：1240

解答：

三次中恰好一次认可有 $\binom{3}{1}=3$ 种方式，每种概率为 $(0.7)(0.3)(0.3)=0.063$ 。

总概率为 $3\cdot 0.063=0.189$ 。

所以正确答案是 B。

Exactly one approval among three occasions arises in $\binom{3}{1}=3$ ways, each with probability $(0.7)(0.3)(0.3)=0.063.$

The total is $3\cdot 0.063=0.189.$

Thus, the correct answer is B.

2008 AMC 10B 第 17 题

答案：B

难度评级：1240

解答：

其他年份的第 17 题