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- Thread starter Alexsandro
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Again lets do some encoding,

Whenever the monkey is successfull in its jump, encode that as a 1 and if it fails encode that as a 0. Hence the sequence of jumps made by the monkey are encoded as a n-bit binary string.

Then the required expectation is the expected longest sequence of 1's in the binary string. This expectation can be calculated from first principles, again a bit tedious.

E[longest sequence of 1's]

= 0 * P(longest sequence of 1's = 0)

+ 1 * P(longest sequence of 1's = 1)

+ 2 * P(longest sequence of 1's = 2)

+...+ n * P(longest sequence of 1's = n)

The probabilities can be calculated by looking that 2^n possible binary representations.

-- AI

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log(n+1)/log(2) fruits

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log(n+1)/log(2) fruits

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