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2008 AMC 10B Problem 17

Problem 17 of 25IntermediateProbability & Statistics

A poll shows that 70%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 (31)=3\binom{3}{1}=3 ways, each with probability (0.7)(0.3)(0.3)=0.063.(0.7)(0.3)(0.3)=0.063. The total is 3⋅0.063=0.189.3\cdot 0.063=0.189. Thus, the correct answer is B.
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Tagged: binomial probability · independent events

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