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S.5 Probability

發問:

Bag X contains 5 black balls, 4 white balls and 3 green balls. Bag Y contains 4 black balls and 3 white balls. A ball is chosen at random from bag X and put into bag Y, and then a ball is drawn from bag Y. Find the probability that the second ball is in bag Y originally, given that it is black. 更新: Let me provide the answer : 48/53 Can anyone provide the procedures?? 更新 2: arthur_cheung2003 : I am sorry!! Your answer is not correct!!! But thanks for your help~~

最佳解答:

http://i49.photobucket.com/albums/f258/cutejohn291/Probability.png From picture, P(Drawing a black ball from X)= (5/12)(5/8)(1/5)=25/480 P(Drawing a black ball from Y)=(7/12)(1/2)(1)=7/24 P(Drawing a black ball from Y | It is a black ball) = (7/24)/(25/480+7/24) = 48/53 2008-01-06 20:20:53 補充： Sorry.From picture, P(Drawing a black ball from X)= (5/12)(5/8)(1/5)=25/480P(Drawing a black ball from Y)=(7/12)(1/2)(1)+(5/12)(5/8)(4/5)=1/2P(Drawing a black ball from Y | It is a black ball) = (1/2)/(25/480+1/2) = 48/53

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