Solution: The probability is 1 / (nCk). This does not depend on a1, ..., an. Thus, for n independent Bernoulli trials, given that there are exactly k successes, the nCk possible sequences consisting of k successes and n − k failures are equally likely. Interestingly, the conditional probability above also does not depend on p (this leads to the notion of a sufficient statistic, which is studied in Stat 111). See iTunes for full solution.

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