Question 4 (1 point) You are at a parade looking up at a large balloon floating directly above the street. You are 60 feet from a point on the street directly beneath
the baloon. To see the top of the baloon, you look up at an angle of 53º. To see the bottom of the ballon you look up at an an angle of 29º.
Estiamte the height, h, of the balloon to the nearest foot. Answer with only the numeric value
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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.