2008 AMC 10B Problem 17

Question

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

Answer: B

Concepts:binomial probability independent events

Difficulty rating: 1240

Small hint:

Exactly one approval can happen in

3

ordered ways

Big hint:

Each such arrangement has probability

(0.7)(0.3)(0.3)

Solution:

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.