SOLUTION: There are two baskets and each of them have 4 white and 8 black marbles. Two random marbles from the basket A have been transfered to the basket B. a) After the transfer what is th

Question 1195022: There are two baskets and each of them have 4 white and 8 black marbles. Two random marbles from the basket A have been transfered to the basket B. a) After the transfer what is the probability of the first marble picked from basket B being white? b) Lets say the first marble was white. What is the probability that when the transfer happened, one black and one white marble were put in basket B
Answer by Edwin McCravy(20062) (Show Source): You can put this solution on YOUR website!

Event E:  2 blacks are transferred at first.
P(E)=(8C2)/(12C2) = 14/33

Event F:
1 black and 1 white are transferred at first.
P(F)=[(4)(8)]/(12C2) = 16/33

Event G: 2 whites are transferred at first.
P(G)=(4C2)/(12C2) = 1/11

Result of E: 4W,10B in basket B
Result of F: 5W,9B in basket B
Result of G: 6W,8B in basket B

P(E then White) = (14/33)(4/14) = 4/33
P(F then White) = (16/33)(5/14) = 40/231
P(G then White) = (1/11)(6/14) = 1/77

P[(E then White) OR (F then White) OR (G then White)] 
= 4/33+40/231+1/77 = 71/231

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P(F|White) = P(F and White)/P(White) =(40/231)/(71/231) =  40/71

Edwin

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