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 \(4\over7\) 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?

This is a tiny bit overdue... please help ASAP!

NotLatePY Nov 26, 2023

#1**0 **

Let f be the probability that a freshman is elected. Then 4f is the probability that a sophomore is elected. Since the sum of the probabilities must be 1, we have f + 4f = 1, which implies f = 1/5. Thus 4f = 4/5. The fraction of the swim team that are sophomores is equal to the probability that a sophomore is elected, which is 4/5. So the answer is 4/5.

parmen Nov 27, 2023