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?

7 comments:

Pax said...

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. ;)

Open Bar said...

"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.

Anonymous said...

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?

Matt Dabney said...

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%.

Anonymous said...

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.

Anonymous said...

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

Anonymous said...

Jerry, no answer? (Before I post the solution)