1985 AHSME Problems/Problem 6
Problem
One student in a class of boys and girls is chosen to represent the class. Each student is equally likely to be chosen and the probability that a boy is chosen is of the probability that a girl is chosen. The ratio of the number of boys to the total number of boys and girls is
Solution
Let the probability that a boy is chosen be , so the probability that a girl is chosen is (as the probabilities must sum to ). Therefore
Now simply notice that the probability a boy is chosen is precisely the proportion of the number of boys out of the total number of students (boys and girls), so the answer is precisely .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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