Suppose you have hired a new worker, unfortunately you do not knowif the worker is a shirker or a hard worker. Suppose working hardraises the probability of making a sale from 40% to 80% (thus raisesthe probability of making a commision C by the same percentage). Ifthe cost of working harder is $200,what commission C should you offerthe worker to provide an incentive to work hard.

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.)