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Question

From a bag containing 9 distinct white and 9 distinct black, 9 balls are drawn at random one by one, the drawn balls being replaced each time. The probability that at least four balls of each colour is in the draw, is

A
A little less than 12
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B
a little greater than 12
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C
12
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D
13
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Solution

The correct option is A A little less than 12
Out of 9 distinct black and 9 distinct white balls, probability of drawing a white ball =12
and drawing black ball is also 12. for at least 4 of each colour in 9 draws with replacement, there are two cases,
Case(i)
P(getting 5 white, 4 black) =9C5 (12)9
Cases (ii)
P(getting 4 white, 5 black) =9C4 (12)9
These are exclusive so
P(atleast 4 of each colour) =9C5 (12)9+9C4 (12)9=63128 which is little less than 12

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