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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.

If the tip varies directly with the number of guest which equation represents between the tip,t, and the number of guest,g?

You coordinate volunteers for litter cleanup in local parks. your spreadsheet lists drivers and the number of seat belts in each driver’s car. the spreadsheet calculates the number of drivers (d) and the total number of seat belts (s). you want to know the maximum number of volunteers, besides drivers, that can be transported to the park in a single trip given that each person must have a seat belt of their own.