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## Homework Statement

A chess master plays n games at a chess competition, each against a different opponent. Based on their past performances, we can estimate the probabilities of each opponent beating the master: p1, . . . , pn ∈ [0, 1]. Describe an algorithm, which given integer k returns the probability that the master wins exactly k out of n games. Then, use it to find the probability of the chess master winning the majority of the games (at least d n 2 e).

## Homework Equations

## The Attempt at a Solution

This time I have a solution. Let k P n denote the probability that he wins k out of n. I came up with the following formula to fill out the table

kPn=(1-Pn)(kP(n-1))+((k-1)P(n-1))Pn

In this case Pn is the prob that he wins and 1-pn that loses

Does that work

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