Consider the student population in a college campus. Assume that 55% of the students are female. Assume that 20% of the male drink and 10% of the female drink.
(a) Pick a female student at random, what is the probability that she does not drink?
10% do drink so 90% do not drink
90% or 0.9
(b) Pick a student at random, what is the probability that the student does not drink?
I am going to let the number of students be x
female = 0.55x number of female non-drinkers = 0.9*(0.55x) = 0.495x
male = 0.45x number of male non-drinkers = 0.8*(0.45x) = 0.36x
Prob that the student doesn't drink = (0.495x+0.36x)/x = 0.495+0.36 = 0.855 or 85.5%
(c) Pick a student at random, what is the probability that this student is male and drinks
male = 0.45x number of male drinkers = 0.2*(0.45x) = 0.09x
prob that this student is male and drinks = 0.09x/x = 0.09 or 9%