Question

A student dormitory at a particular college consists of the following: I. 40% are freshman of whom 15% own a car 2. 30% are sophomores of whom 25% own a car 3. 20% are juniors of whom 40% own a car 4. 10% are seniors of whom 60% own a car. A student is randomly selected from the dormitory a. Find the probability that a student owns a car. b. Ifa student owns a car, find the probability that the student is a junior. c. If a student does not own a car, find the probability that the student is a freshman

Answer 1

Here we have

(a)

P(student owns a car) =P(freshman and owns a car)+P(sophomores and owns a car)+P(juniors and owns a car)+P(seniors and owns a car)=0.4*0.15+0.3*0.25+0.2*0.4+0.1*0.6=0.275

b) P(student is a junior given owns a car) =P(juniors and owns a car)/P(owns a car)

=0.2*0.4/0.275=0.2909

c) P(student is a freshman given not own a car) =P(freshman and not own a car)/P(not own car)

=0.4*(1-0.15)/(1-0.275)=0.4690