Question

Among undergraduate students living on a college campus, 20% have an automobile. Among undergraduate students living off campus, 60% have an automobile. Among undergraduate students, 30% live on campus. Given the probabilities of the following events when a student is selected at random:
(a) Student lives off campus.
(b) Student lives on campus and has an automobile.
(c) Student lives on campus and does not have an automobile.
(d) Student lives on campus and/or has an automobile.
(e) Student lives on campus given that he/she does not have an automobile.

Answer 1

Answer: a) 70%

b) 6%

c) 24%

d) and: 6%

   or: 66%

e) 46.2%

Step-by-step explanation:

Living on campus = 30%

Living off Campus = 70%

                                           

Living on campus with car = 20% of 30% = 0.2 x 0.3 = 0.06 = 6%

Living on campus w/o car = 80% of 30% = 0.8 x 0.3 = 0.24 = 24%

Living off campus with car = 60% of 70% = 0.6 x 0.7 = 0.42 = 42%

Living off campus w/o car = 40% of 70% = 0.4 x 0.7 = 0.28 = 28%

a) 70%

b) 6%

c) 24%

d) Student lives on campus and has an automobile: 6%

   Student lives on campus or has an automobile = 66%

living on campus 30%

students with car = 6% (on campus)  42% (off campus)

30 - 6 + 42 = 66

e) P (living on campus/not have a car) = P(living on campus w/o a car)/P(not have a car)

P(living on campus w/o a car) = 24

P(not have a car) = 24+28 = 52

P (living on campus/not have a car) = 24/52 = 0.462 = 46.2%