Consider the following information about travelers (based partly on a recent Travelocity poll): 40% check work e-mail, 30% use a cell phone to stay connected to work, 25% bring a laptop with them, 23% both check work e-mail and use a cell phone to stay connected, and 51% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. Finally, 88 out of every 100 who bring a laptop check work e-mail, 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 e-mail 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 a randomly selected traveler checked work e-mail and brought a laptop, what is the probability that s/he uses a cell phone to stay connected?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.

The host of a game show is holding a bag with chips to see what prizes the contestants will play for. five (5) of the chips say “new car” ten (10) of the chips say “new tv” three (3) of the chips say “trip to france” contestant named “patty” reaches into the bag. a. what is the probability of choosing a tv chip? b. what is the probability of choosing a car chip next without replacing the 1st chip? c. are these dependent or independent events?