Assume that, for every batter on a baseball team, there is a 65% chance of making an out in every plate appearance. If plate appearances constitute independent trials... (a) what is the probability that 27 straight batters make outs? (This is the probability that a starting pitcher throws a "perfect game".) Over the course of a major league baseball season, each of the 30 teams plays 162 games; this means that there are 30x162-4860 starting pitchers used each season. (b) Find the probability that there is at least one "perfect game" pitched over the course of an entire baseball season.

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