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In a certain game, what is the probability that Martha wins

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In a certain game, what is the probability that Martha wins

by varun289 » Wed May 01, 2013 12:14 am
In a certain game, what is the probability that Martha wins the first 5 rounds and loses the sixth?

The chance that Martha wins the first 4 rounds and loses the fifth is 1/32.
The chance that Martha wins the first 6 rounds and loses the seventh is .1/128
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by Matt@VeritasPrep » Wed May 01, 2013 10:23 pm
This question seems a little shoddy: if the odds that she wins any given round are the same, then the answer is C; if the odds vary, then the answer is E.

Assuming that Martha's odds of winning any given round are the same (and that there are no ties!) ...

Let w be the odds of Martha winning a given round and (1 - w) be the odds of Martha losing a given round. Statement (1) gives us w * w * w * w * (1-w) = 1/32. This has two real, positive solutions, but the methods for arriving at the second (i.e. the answer that is NOT w = 1/2) are beyond the GMAT. Same issue with Statement (2). Together we have w * w * w * w * (1-w) = 1/32 and w * w * w * w * w * w * (1-w) = 1/128. The only solution is the obvious one: w = 1/2.

Of course, we probably can't assume that the odds are the same each round and that there are no ties, meaning we are out of luck.

This question feels outdated to me: a few years back the GMAC loved superficially "easy" DS probability questions that turned out to be missing certain key components, but I'm not sure they test that much these days.
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