Question 1092787: Probability Part 1.
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There are two bags.
[Bag 1] contains 4 white and 2 black balls.
[Bag 2] contains 5 white and 4 black balls.
2 balls are choosen at random from [Bag 1] and dropped into [Bag 2]. 1 ball is then taken from [Bag 2].
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Ques: What's the probability that the ball taken from [Bag 2] is a white ball??
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...Let's see who's human enough...
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! One possibility with probability (4/6)(3/5) or 0.4, is both balls are white, and the probability the ball taken from bag 2, with 7/4 is 7/11. The joint probability of this is 7/11*2/5=14/55 or 42/165.
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Second possibility is both balls are black with probability (2/6)(1/5)=1/15. Now bag 2 has 5/6, and the probability of a white is 5/11, so joint probability is 5/165.
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Third possibility is one is white and one is black. There are two ways this can occur: 1 is (4/6)(2/5)=8/30.
The other is (2/6)(4/5)=8/30. This accounts for the rest of the possibilities (add to 1).
Now bag 2 has 6/5, and the probability of a white ball is 6/11*8/15=48/165.
The answer is 95/165 or 19/33.
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