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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 $4/7$ 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?

 

The Answer is not 3/5, thank you! :)

 Oct 29, 2023
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Letxbe the fraction of the swim team that are sophomores. Then, the fraction of the swim team that are freshmen is1−x.

We are given that the probability that a sophomore is elected is4/7times the probability that a freshman is elected. This can be expressed mathematically as follows:

P(\text{sophomore}) = 4/7 \cdot P(\text{freshman})

We are also given that each member is equally likely to be elected, which means that the probability of a sophomore being elected is equal to the probability of a freshman being elected plus the probability of a sophomore being elected. This can be expressed mathematically as follows:

P(\text{sophomore}) = P(\text{freshman}) + P(\text{sophomore})

Substituting the first equation into the second equation, we get:

4/7 \cdot P(\text{freshman}) = P(\text{freshman}) + P(\text{sophomore})

Combining like terms, we get:

3/7 \cdot P(\text{sophomore}) = P(\text{freshman})

Dividing both sides byP(freshman), we get:

3/7 \cdot x = 1-x

Solving forx, we get:

x = \frac{7}{10}

Therefore, 7/10 ​​of the swim team are sophomores.

 Oct 29, 2023

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