SOLUTION: STATISTICS. You shuffle a deck of playing card, and then start turning the cards one at a time. The first one is black. The second one is also a black card. So is the third, and th

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: STATISTICS. You shuffle a deck of playing card, and then start turning the cards one at a time. The first one is black. The second one is also a black card. So is the third, and th      Log On

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Question 1113532: STATISTICS. You shuffle a deck of playing card, and then start turning the cards one at a time. The first one is black. The second one is also a black card. So is the third, and this happens up to the 10th card. You start thinking “the next one will likely be red!”. Are you correct in this reasoning?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
there are 26 red cards and 26 black cards in the deck
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you have turned over 10 black cars, that leaves 16 black cards in the deck and 42 cards in the deck
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Probability (P) of drawing 10 black cards is (26/52) * (25/51) * (24/50) * (23/49) * (22/48) * (21/47) * (20/46) * (19/45) * (18/44) * (17/43) = 0.0003
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P of drawing 11 black cards is 0.0003 * (16/42) = 0.000114286
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P of drawing 10 black cards and the 11th is a red card = 0.0003 * (26/42) = 0.000185714
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No - there is a small chance that the next card drawn will be red
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