A bag contains 10 white and 3 black balls. Ball are drawn one by one withput replacement till all the black balls are drawn. Find the probability that all the black balls are drawn by 6th draw.
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The required event is we drawn 2 black balls and 3 white balls in the first 5 draws and the last third black ball is drawn in the 6th draw.
Probability that we get a black ball in the 6th draw is 1/8,
because there are only 8 balls and only one black ball is drawn in the 6th draw.
Probability of drawing 2 black balls and 3 white balls in the first 5 draws = 3C2.10C3/13C7
Therefore the required probability = [1/8]. 10C3.3C2/13C7 = 0.0350
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