6. 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.