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moonman239

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## Homework Statement

Suppose that Amy tells Bob to guess the number she's thinking of. This number can be anywhere between 1 and 100. Amy allows Bob as many guesses as he needs. Each time Bob randomly guesses the number, Amy tells him whether his guess is too low, too high, or correct.

Given that information, what is the probability that:

1) it will take Bob at most 6 guesses

2) it will take Bob at most 30 guesses

## Homework Equations

## The Attempt at a Solution

Well, this is not really a solution, but let me tell you what I know about the problem so as to help someone give me a solution: The probability of guessing the number correctly changes, because Bob will always change his guess based on Amy's clues. For example, if Bob guesses 36, and Amy tells him that guess is "too high," Bob then knows that Amy's number is somewhere between 1 and 35. Then the probability of guessing the number correctly is 1/34.

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