Probability of an event

Question

The grades of a freshman college class, obtained after the first year of college, were analyzed. Seventy percent of the students in the top quarter of the college class had graduated in the upper 10% of their high school class, as had 50% of the students in the middle half of the college class and 20% of the students in the bottom quarter of the college class.

a. What is the probability that a randomly chosen freshman graduated in the upper 10% of his high school class?

b. What is the probability that a randomly chosen freshman who graduated in the upper 10% of the high school class will be in the top quarter of the college class?

c. What is the probability that a randomly chosen freshman who did not graduate in the upper 10% of the high school class will not be in the top quarter of the college class?

Answer 1

a) .25 * .7 + .5 * .5 + .2 * .25 = .475 = 19/40

b) .25 * .7/.475 = .175/.475 = 7/19 = .3684

c) 1 - P(in top quarter) = 1 - .25 * .3/(1 - .475) = 1 - .075/.525 = 1 - 1/7 = 6/7 = .8571