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A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $\frac{4}{7}$  times the probability that a freshman is elected. Everyone on the junior varsity swim team is either a freshman or sophomore. What fraction of the swim team are sophomores?
 

 Apr 7, 2023
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Let x be the fraction of the swim team that are sophomores.

The probability that a sophomore is elected is 4/7 times the probability that a freshman is elected. This means that the probability that a freshman is elected is 7/11 times the probability that a sophomore is elected.

The probability that a freshman is elected is 1 - x, since the probability of a freshman being elected is 1 minus the probability of a sophomore being elected.

Therefore, we have the following equation:

4/7 * 7/11 * x = 1 - x

Solving for x, we get:

x = 3/5

Therefore, 3/5 of the swim team are sophomores.

 Apr 7, 2023

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