# Fast Baseball Pitcher

Discrete Mathematics Level pending

A baseball team hires a pitcher who throws so fast that no one could ever hit his pitches. Instead, he either strikes out or walks every batter. He strikes out any given batter with probability $$p.$$ To have an earned run average less than $$1.00,$$ what is the minimum possible value of $$p?$$

Details: In baseball, there are 9 innings. An earned run average is the number of runs given up per 9 innings. After 3 people are walked, each additional walk scores a run. After 3 strike outs, the inning ends.

Note: While the majority of this problem can be solved with combinatorics, you may need a computing device for the last step.

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