2008 AMC 10B Problem 17

Problem 17 of 25IntermediateCounting & Probability

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?

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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.

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