Qusetion: Some information regarding the composition of the student athlete population in the high school mentioned in Exercise is given in the table below. For example, 65% of the student athletes are male, 50% of the student athletes play basketball, and female athletes do not play football. For a student athlete selected at random, the events F = {the student athlete is female} and T= {the student athlete prefers track} are independent.
(a) Fill in the remaining entries of the above table.
(b) If a randomly selected student athlete prefers basketball, what is the probability that the student athlete is female?
(c) Are the events F and B= {the student athlete prefers basketball} independent?
Exercise: An athlete is selected at random from the population of student athletes in a small private high school, and the athlete's gender and sports preference is recorded. Define the events M = {the student athlete is male}, F = {the student athlete is female}, and T= {the student athlete prefers track}. We are told that the proportion of male athletes who prefer track is the same as the proportion of student athletes who prefer track or, in mathematical notation, P(T|M) = P(T). Can we conclude that the proportion of female athletes who prefer track is the same as the proportion of student athletes who prefer track, or P(T|F) = P(T)? Justify your answer.