Tuesday, April 21, 2009
Math Question of the Day
Suppose a baseball team has hitters who only gets singles or strikes out. Suppose further that when a batter gets a single, if there is already a man on first base he advances to second base, while any runner on second or third base scores a run. When a batter strikes out, any players on base stay at that base. Finally, suppoe that all the batters have equal hitting ability. If the probability of each batter getting a hit is 50%, what is the probability of the team scoring at least one run before having 3 outs?
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7 comments:
50%.
To score a run they need 3 hits before they get 3 outs. One hit to get a guy on first, one to advance him to second, and a third to score.
This of course assumes they aren't playing the Mets and Pedro Feliciano isn't balking in runs. ;)
"If the probability of each batter getting a hit is 50%"If everyone on your team is batting .500, there's no way you're ever going to lose. You will score lots and lots and lots of runs.
Wow, Open Bar, I never knew you ever looked at my blog. I was an admirer of yours for a while. I feel worthy.
Anyway, so are you going up on Pax's 50%? Any other guesses?
Pax touched on something, but didn't follow up with it.
Are we to assume the only way the runner on base can advance is via a hit by his teamate? Runners can advance on a stolen base, error, balk, etc.
I'd say the chances of scoring are higher than 50%.
Runners can only score as assumed in the question. Only singles or strike out (50-50 possibility of each). Only advancing as written.
It's strictly a math question, not a baseball question.
In response to Hollywood,
If Pax’s theory is right (which I think it is) then you would score once, every other inning. Thus, you would average 4.5 runs per game. I don’t watch a lot of baseball but 4.5 runs does not seem like lots of runs. I think the problem with Chris’s theory of each batter hitting .500 resulting in lots of runs is because each batter is only hitting a single and you can score runs other ways, errors, stolen bases, etc…
Evan
Jerry, no answer? (Before I post the solution)
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