2008 AMC 10B Problems/Problem 17

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Problem

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?

$\mathrm{(A)}\ {{{0.063}}} \qquad \mathrm{(B)}\ {{{0.189}}} \qquad \mathrm{(C)}\ {{{0.233}}} \qquad \mathrm{(D)}\ {{{0.333}}} ...$

Solution

The pollster could select responses in 3 different ways: YNN, NYN, and NNY, where Y stands for a voter who approved of the work, and N stands for a person who didnt approve of the work. The probability of each of these is $(0.7)(0.3)^2=0.063.$ Thus, the answer is $3 \cdot 0.063=0.189\Rightarrow \boxed{B}$

2008 AMC 10B (Problems • Resources)
Preceded by Problem 16	Followed by Problem 18
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2008 AMC 10B Problems/Problem 17

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