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Sunrise Problem
Entry Nr. 3268, by user 1
A system gave nr_answers answers. All were correct. What is the expected failure rate of the system?

Laplace:

expected failure rate = (nr_answers+1)/(nr_answers+2)

http://en.wikipedia.org/wiki/Rule_of_succession

Upper bound:

error_rate=0.1
correct_answers=8

prob=Math.pow((1-error_rate),correct_answers)

laplace=(correct_answers+1)/(correct_answers+2)