Joe and Jane are at a carnival. Joe gets on the large Ferris wheel at the same time Jane gets on the small Ferris wheel. The rides begin at the same time. The large Ferris wheel takes 25 seconds to make one revolution and the small Ferris wheel takes 10 seconds to make one revolution. Part A How many seconds will pass before Joe and Jane are both at the bottom again?Part B How many revolutions will the large ferris wheel take before Joe is at the bottom again? Part C How many revolutions will the small ferris wheel take before Jane is at the bottom again?

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.