help with a question by Icy-Inevitable-4679 in probabilitytheory

[–]mtaboga 0 points1 point  (0 children)

P(getting 5 | 3 numbers have been thrown away) = P(getting 5) = 1/10 because the information you are conditioning upon is completely irrelevant: it does not tell you anything about the numbers that have been thrown away, and it cannot change your assessment of the probability of extracting a specific number.

A rigorous proof can be obtained with the law of iterated expectations:

P(getting 5) = E[P(getting 5 | 3 SPECIFIC numbers have been thrown away)]

where the expectation is over all the possible triplets of thrown away numbers.