A bag contains 10 black and 5 white balls. Two balls are drawn from the bag succes- sively whithout replacement. Find the probability that both the balls drawn are black.
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They are two ways of picking balls of alternating colours. You could draw WBWB or BWBW.
The probability of picking WBWB is (10/16)x(6/15)x(9/14)x(5/13) and of picking BWBW is (6/16)x(10/15)x(5/14)x(9/13).
Both probabilities are equal to 2700/4368 or 45/728.
Therefore 45/728+45/728 = 45/364.
This is equal to about a 12.36% chance of picking balls of alternating colours
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