A survey of 500 consumers revealed the following preferences

A survey of 500 consumers revealed the following preferences for getting rides to city destinations: 290 reported using Uber^TM, 220 reported using a taxicab service, and 110 reported using both. What is the probability that a randomly selected consumer reported using either Uber^TM or a taxicab service to get around in the city? Show work. Let U = {consumers who reported using Uber} and T = {consumers who reported using a taxicab service}. Determine the number of consumers belonging to each of the regions I, II, III, IV. Region I:_Region II:_Region III:_Region IV:_

Solution

(a) The formula for the event A or the event B occuring is P(A U B) = P(A) + P(B) – P(A B). Here P(A) = 290/500 = 0.58, P(B) = 220/500 = 0.44 and P(A B) = 110/500 = 0.22. Therefore, the probability that a randomly selected consumer reported using either Uber or a Taxicab service to get around the city is P(A) + P(B) – P(A B) = 0.58 + 0.44 – 0.22 = 0.8.

(b) Region I = U – ( U T) = 290 – 110 = 180. Region II = U T = 110, Region III = T - ( U T) = 220 – 110 = 110, Region IV = 500 – ( U U T) = 500 – ( 290 + 220 -110) = 500 -400 = 100.