Difference between revisions of "2021 Fall AMC 10A Problems/Problem 10"
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\end{align*}</cmath> | \end{align*}</cmath> | ||
Therefore, the answer is <math>t-s=\boxed{\textbf{(B)}\ {-}13.5}.</math> | Therefore, the answer is <math>t-s=\boxed{\textbf{(B)}\ {-}13.5}.</math> | ||
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Revision as of 18:20, 22 November 2021
Problem
A school has students and teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are and . Let be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is ?
Solution
The formula for expected values is We have Therefore, the answer is
~MRENTHUSIASM