18. The servicing of a machine requires two separate steps, with the time needed for the first step being an exponential random variable with mean 0.2 hour and the time for the
second step being an independent exponential random variable with mean 0.3 hour. If a
repair person has 20 machines to service, what is approximately the probability that all the
work can be completed in 8 hours?

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)