Balls in a Bag

There are 10 coloured balls in a bag. 7 are red and 3 are blue. You remove one ball and, without replacing the first, then remove a second.

If the second ball is blue, the probability that the first ball was red can be written as a b \frac{a}{b} where a a and b b are positive, co-prime integers. Calculate the value of a + b a + b .


The answer is 16.

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1 solution

Arijit Banerjee
Mar 18, 2014

on applying BAYE's theorem we get = ( (7C1/10C1) *(3C1/9C1) / ( (7C1/10C1) *(3C1/9C1) + (3C1/10C1 * 2C1/9C1))) = 7/9 = 7 + 9 =16

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