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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  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?

Jun 11, 2024

#1
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You have a missing number in your question, but I think that I can still solve it. If all the members are equally likely to be elected as President, then it doesn't matter if you are a freshman or sophomore. So, your missing number is that there are ___ times more sophomores than freshmen. If your missing number was 2, then there are twice as many sophomores then freshmen. So, the fraction of the team that is sophomores is 2/3. Does this help? If you can give me the missing number, then I can solve it more completely.

Jun 11, 2024
#2
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I found the original question from where this was posted.

The missing number is 3/2.

If the number is 3/2, then we can do the problem the following.

Since there are 3/2 times more sophomore, using f for number of freshmen, we can write

\(f+3/2f = 1\\ 5/2f=1\\ f = 2/5\)

So 2/5 of the team is freshmen.

The other \(1-2/5=3/5\) of the team are sophomores.