Answer to Question #281285 in Statistics and Probability for Thoma

Question

Among 200 persons interviewed as part of an urban mass transportation study, some live more than 5 miles from the center of the city (X), some now regularly drive their own car to work (Y), some would gladly switch to public mass transportation if it were available (Z). Use the information given in the below figure to find the probabilities the person

a) Lives more than 5 miles from the center of the city

b) Lives more than 5 miles from the center of the city given that he or she would gladly switch to public mass transportation

c) Regularly drives his or her car to work given that he or she lives more than 5 miles from the center of the city

d) Would not want to switch to public mass transportation given that he or she does not regularly drive his or her car to work

Answer 1

Diagram is missing in the problem.

The diagram is

Solution:

a)

The shaded portion refers to lives more than 5 miles from the center of the city,

Total lives = 12+30+60+8 = 110

b)

The shaded portion refers to lives more than 5 miles from the center of the city given that he/she would gladly switch to public mass transportation.

Total lives = 60+8 = 68

c)

The shaded portion refers to lives who regularly drives his or her car to work given that he/she lives more than 5 miles from the center of the city

Total lives = 30+60 = 90

d)

The shaded portion refers to would not want to switch to public mass transportation given that he/she does not regularly drive his/her car to work

Total lives = 31+12 = 43