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There are 3 white, 3 red and 5 black balls in a box. By chance, three...

There are 3 white, 3 red and 5 black balls in a box. By chance, three balls are taken out from the box. The person wins 1 dollar when taking out a white ball but loses 1 dollar when taking out a red ball. X is an event, describing the amount of money that was won (lost) in one try. What values does X have and what are the probabilities of those values? What is the probability that the money will be won, i.e. P(X>=1)?

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Answer #1

probability that the money will be won P(X>=1)=P(1 white and 2 black balls)+P(2 white and 1 black balls)+P(2 white and 1 black ball)+P(3 white balls=3C1*5C2/11C3+3C2*3C1/11C3+3C2*5C1/11C3+3C3/11C3 =55/165 =1/3

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