2008 AMC 10B Problem 17

Below is the professionally curated solution for Problem 17 of the 2008 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10B solutions, or check the answer key.

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Concepts:binomial probability independent events

Difficulty rating: 1240

17.

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?

$0.063$

$0.189$

$0.233$

$0.333$

$0.441$

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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