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I need to compute probability

 

 

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  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?

 Mar 6, 2023
 #1
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Lets say we have 10 people on the team. Because the probabilities of choosing a sophomore or a freshman are the same, that means that they both have a 50/50 chance and that there are the same amount of freshman and sophomores on the team. Therefore the fraction of the swim team that are sophomores are 1/2.

Hope this Helps!
 Mar 6, 2023
 #2
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Let p be the probability that a sophomore is elected and q be the probability that a freshman is elected. Since every member is equally likely to be elected, we have:

 

p + q = 1 (the sum of probabilities of all possible outcomes is 1)

We are also given that:

 

p = q (the probability of a sophomore being elected is equal to the probability of a freshman being elected)

Substituting q for p in the first equation, we get:

 

2p = 1

Therefore, p = 1/2 and q = 1/2. This means that the probability of a sophomore being elected is equal to the probability of a freshman being elected and that half of the members are sophomores and half are freshmen.

 

Therefore, the fraction of the swim team that are sophomores is 1/2.

 Mar 6, 2023

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