**Question**: A manager is planning to use three pitchers tomorrow Tom, Fred and Bill. He is planning to pitch Tom for five innings, Fred for three innings, and Bill for one inning. Tom has a 3.1 ERA, Fred has a 4.0 ERA, and Bill has a 2.7 ERA. What is the expected number of earned runs the team is likely to give up tomorrow?

**Answer**: The expected number of earned runs given up by the three pitchers in 9 innings is a weighted average of the three ERAs where the weights are the fraction of the game each pitcher pitches.

Expected runs given up =

(5/9)x3.1+(4/9)x4.0+(1/9)x2.7

=3.8

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