1. The undergraduate student body at UT is broken down into the following years: 31% are freshmen, 27% are sophomores, 20% are juniors, and 22% are seniors (or higher). 18% of sophomores, 22% of juniors, and 28% of seniors have attended at least one football game. a. If 22% of the entire undergraduate body has attended a football game, what percent of freshmen have gone to a game? Pr[game] = Pr[game | freshman]Pr[freshman] + Pr[game | soph]Pr[soph] + Pr[game | jr]Pr[jr] + Pr[game | sr]Pr|[sr] .22 = Pr[game | freshman] (.31) + (.18)(.27) + (.22)(.20) + (.28)(.22) .22 = Pr[game |freshman] (.31) +.0486 +.044 + .0616 .22 = Pr[game | freshman] (.31) +.1542 .0658 = .31Pr[game | freshman] Pr[game | freshman] =.2126 Draw a probability tree of the above information. (Include the number you found in parta.) If you find a random student who has never attended a football game, what is the probability that they are a freshman? Pr[fresh | no game] = (Pr[no game | freshman]Pr[freshman]) / Pr[no game] In part a, you learned that 22% of the student body has gone to a game. Thus, (1 - .22), or.78, have not gone to a game. Pr[fresh | no game] = (1-.2126)*(.31) /.78 =.3129
