AMC10 2008 B

AMC10 2008 B · Q17

AMC10 2008 B · Q17. It mainly tests Probability (basic).

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?

一项民调显示，70%的选民赞成市长的表现。民调员在三个不同的场合随机选择一名选民。恰好在这三个场合中的一个场合该选民赞成市长的表现的概率是多少？

(A) 0.063 0.063

(B) 0.189 0.189

(D) 0.333 0.333

(E) 0.441 0.441

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): The responses on these three occasions, in order, must be YNN, NYN, or NNY, where Y indicates approval and N indicates disapproval. The probability of each of these is $(0.7)(0.3)(0.3)=0.063$, so the requested probability is $3(0.063)=0.189$.

答案（B）：这三次的回答按顺序必须是 YNN、NYN 或 NNY，其中 Y 表示赞成，N 表示反对。每一种情况的概率为 $(0.7)(0.3)(0.3)=0.063$，所以所求概率是 $3(0.063)=0.189$。

Topics

CP.006 Probability (basic)