A bag contains six balls of different colours. Two balls are drawn...

Given,

A bag contains six balls of different colours, two balls are drawn in succession with replacement,

The probability that both the balls are of the same colour will be $p = \dfrac{6}{36}$

Now Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$,

So, probability will be $q = \dfrac{C1 6 \times C1 5 \times C1 4}{{6}^{4}} = \dfrac{120}{1296} = \dfrac{5}{54}$

Now the ratio of $p \text{ and } q$ will be $\dfrac{p}{q} = \dfrac{9}{5}$

Now, on comparing with $\dfrac{p}{q} = \dfrac{m}{n} ⇒ m + n = 14$