Consider the following information about travelers on vacation (based partly on a recent Travelocity poll): 40% check work email, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 23% both check work email and use a cell phone to stay connected, and 51% neither check work email nor use a cell phone to stay connected nor bring a laptop. In addition, 88 out of every 100 who bring a laptop also check work email, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop. a. ?What is the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected? b. ?What is the probability that someone who brings a laptop on vacation also uses a cell phone to stay connected? c. ?If the randomly selected traveler checked work email and brought a laptop, what is the probability that he/she uses a cell phone to stay connected?

Solution : Step 1: From the given data 40% of travelers check work email, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 23% both check work email and use a cell phone to stay connected, and 51% neither check work email nor use a cell phone to stay connected nor bring a laptop. It is also given that 88 out of every 100 who bring a laptop also check work email, and 70 out of every 100 who use a cell phone to stay connected also bring a laptop. Step 2 : a) We have to find the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected. Lets define the events as A: the travelers check work email B: The travelers use cell phone to get connected C: The travelers brings laptop with them . From the given informations it is clear that P(A)= .4 P(B)=.3, P(C)= .25 P(AB)=P(travelers using both work email and cell phones to get connected)= 0.23 P(A C = P(neither check work email nor use a cell phone to stay connected nor bring a laptop)= 0.51 P(C/B)= P(The travelers check work email given that they bring laptop) =0 .7 P(A/C) =P( The travelers who bring a laptop given that they use cell phone ) = .88 So the probability that a randomly selected traveler who checks work email also uses a cell phone to stay connected P( AB) = 0.23