Although this problem may look like homework, I assure you it is not. It is a question that arose from a trading card game that I am stuck on. The problem is as follows (with simplified cards)(adsbygoogle = window.adsbygoogle || []).push({});

You have a deck of 53 cards, and 11 of those cards are red and 42 are black. If you were to randomly draw 7 cards from the deck, how often would your hand of 7 have *less* red cards in it if you had removed 1 red card from the deck prior to drawing your cards compared to leaving it in?

I'm fairly certain this is a hypergeometric distribution and I have calculated the probabilities of drawing 0-7 red cards in a hand of 7 with 11 red cards in a 53 card deck as well as the probability of drawing 0-7 red cards in a hand of 7 with 10 red cards in a 52 card deck. These numbers are listed below. Where to go from here I am not sure. This seems to be a conditional probability but there shouldn't be any dependence since the 7 drawn cards are replaced on each trial.

Code (Text):

0 1 2 3 4 5 6 7

53 17.50% 37.44% 30.35% 11.98% 2.46% 0.26% 0.01% 0.00%

52 20.17% 39.21% 28.61% 10.04% 1.80% 0.16% 0.01% 0.00%

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# Conditional Probability in a card game

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