Question: A fair die having two faces coloured blue, two red and two green, is thrown repeatedly. Find the probability that not all colours occur in

A fair die having two faces coloured blue, two red and two green, is thrown repeatedly. Find the probability that not all colours occur in the first k throws.

Deduce that, if N is the random variable which takes the value n if all three colours occur in the first n throws but only two of the colours in the first n − 1 throws, then the expected value of N is 11

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