Re: A card game probability

On Jan 25, 9:25 pm, "jsepp...@xxxxxxxxx" <jsepp...@xxxxxxxxx> wrote:
Take a card deck with 52 cards. Pick cards one by one and compute the
cards by ace, two, three,..., jack, queen, king, ace,..., king, ace,
..., king, ace, ..., king. What is the probability that at least once
you turn a card of the same value as you say aloud?

The probability that you turn the first card of the same value as one
of the n cards turned before exactly in your (n+1)-st trial is

p_n = 3n/(52-n) prod_{j=1}^{n-1}(1-3j/(52-j)).

Hence, the probability that you turn such a card in n trials is

sum_{j=1}^{n-1} p_j.

Regards,
Faton Berisha

.

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