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Four marbles are drawn simultaneously and at random from an urn containing 8 black, 7 white,...

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Basic Math

Four marbles are drawn simultaneously and at random from an urncontaining 8 black, 7 white, and 5 red marbles.

What is the probability that at least one of them is white?

Answer & Explanation Solved by verified expert
4.0 Ratings (761 Votes)

P(at least one is white) = (7C1 * 13C3 + 7C2 * 12C2 + 7C3 * 12C1 + 7C4)/20C4

                                     = (7!/(1! * 6!) * 13!/(3! * 10!) + 7!/(2! * 5!) * 12!/(2! * 10!) + 7!/(3! * 4!) * 12!/(1! * 11!) + 7!(4! * 3!))/(20!/(4! * 16!) = 0.7932

  

                                                             

                                                   
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