Difference between revisions of "2023 SSMO Speed Round Problems/Problem 7"
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Revision as of 14:18, 3 July 2023
Problem
At FenZhu High School, th graders have a 60\% of chance of having a dog and th graders have a 40\% chance of having a dog. Suppose there is a classroom of th grader and th graders. If exactly one person owns a dog, then the probability that a th grader owns the dog is for relatively prime positive integers and Find
Solution
The probability that a th grader has the only dog is and the probability for an th grader is
Then,
The probability is thus so the sum is