Question

A mathematics class consists of 40% freshmen, 30% sophomores, 20% juniors, and 10% seniors.If 50% of the freshmen, 60% of the sophomores, 70% of the juniors, and 80% of the seniors are males, what is the probability that a randomly selected male student is a freshman?

Answer 1

P(freshmen) = 0.4

P(sophomores) = 0.3

P(juniors) = 0.2

P(seniors) = 0.1

P(male | freshmen) = 0.5

P(male | sophomores) = 0.6

P(male | juniors) = 0.7

P(male | seniors) = 0.8

P(male) = P(male | freshmen) * P(freshmen) + P(male | sophomores) * P(sophomores) + P(male | juniors) * P(juniors) + P(male | seniors) * P(seniors)

             = 0.5 * 0.4 + 0.6 * 0.3 + 0.7 * 0.2 + 0.8 * 0.1

             = 0.6

P(freshman | male) = P(male | freshmen) * P(freshmen) / P(male)

                               = 0.5 * 0.4 / 0.6

                               = 0.333