Question 6(Multiple Choice Worth 6 points)

(07.02 LC)

The picture below shows a right-triangle-shaped charging stand for a gaming system:

The side face of a charging stand is a right triangle labeled ABC. The measure of angle ACB is 90 degrees and the measure of angle ABC is 50 degrees. Side B C measures 3 inches.

Which expression shows the height, AC, of the charging stand?

3 divided by cos 50 degrees
3 tan 50°
3 divided by tan 50 degrees
3 cos 50°

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.