Three bags A, B, C are given. Bag A contains m blue balls, bag B contains n green balls, bag C contains P red balls and $\min {m, n, p} \geq 7.$ A fair dice is rolled. If outcome is 1 or 2 then one ball from A is drawn. If outcome is 3 or 4 then one ball from B is drawn. If outcome is 5 or 6 then one ball from C is drawn. This drawn ball is put into bag D which is initially empty. This process is repeated six more times and after that one ball is drawn from D.

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The probability that the final drawn ball from D is blue is dependent on m, n, p.

The probability that the final drawn ball from D is blue is independent of m, n, p

Given that the final drawn ball is blue, the probability that D contains balls of each colour and equal number of green and red balls is dependent on m, n, p.

Given that the final drawn ball is blue, the probability that D contains balls of each colour and equal number of green and red balls is $\frac{140}{729} .$

answer is B, C.

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