Captain William has a ship that HMS Crimson Lynx. the ship is 5 furlongs from The Dread pirate Emily and her merciless Band of Thieves. if his ship has already been hit, Captain William as probability 1/3 of hitting the pirate ship. if his ship has been hit, Captain William will always miss. if her ship hasnt already been hit, dread pirate Emily has probability 1/7 of hitting the captain's ship. if her ship has been hit, dread pirate emily will always miss. if the captain and the pirate each shoot once and the captain shoots first what is the probability that the captain hits the pirate ship but the pirate Misses

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.