Problem
Greg Pickett, coach of a little-league baseball team, is preparing for a series of four games against four good opponents. Greg would like to increase the probability of winning as many games as possible by carefully scheduling his pitchers against the teams they are each most likely to defeat. Because the games are to be played back to back in less than one week, Greg cannot count on any pitcher to start in more than one game.
Greg knows the strengths and weaknesses not only of his pitchers but also of his opponents, and he believes he can estimate the probability of winning each of the four games with each of the four starting pitchers. Those probabilities are listed in the table at the top of the next column.
What pitching rotation should Greg set to provide the highest sum of the probabilities of winning each game for his team?