For the given pair of events, classify the two events as independent or dependent. a. Driving in a remote area
b. Finding that you don't have cellphone service
Choose the correct answer below.
A. The two events are independent because the occurrence of one affects the probability of the occurrence of the other.
B. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other.
C. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other.
D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other.

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.