Rule of Succession - Statement of The Rule of Succession

Statement of The Rule of Succession

If we repeat an experiment that we know can result in a success or failure, n times independently, and get s successes, then what is the probability that the next repetition will again be a success?

More abstractly: If X1, ..., Xn+1 are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them,

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