Regina is buying a new car. She sees two advertisements in the paper for the same car at two different prices from two different dealerships. Both dealers are offering a simple-interest loan for the price of the car. A photo of car includes two ads. Ad A shows the vehicle priced at twenty-four thousand two hundred dollars at six point five percent interest and an unknown number of years. Ad B shows an unknown price, at a five point three percent interest over nine years. Question 1 Part A Regina calculates that to buy the car in Ad A, the loan would ultimately cost her $41,503. Over how many years is the loan in Ad A to be paid back?

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.