2008 AMC 10B Problems/Problem 17
Problem
A poll shows that 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?
Solution 1
Letting Y stand for a voter who approved of the work, and N stand for a person who didn't approve of the work, the pollster could select responses in different ways: . The probability of each of these is . Thus, the answer is
Solution 2
In more concise terms, this problem is an extension of the binomial distribution. We find the number of ways only 1 person approves of the mayor multiplied by the probability 1 person approves and 2 people disapprove:
Video Solution by TheBeautyofMath
With explanation of how it helps on future problems, emphasizing "Don't Memorize, Understand" https://youtu.be/PO3XZaSchJc
~IceMatrix
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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