### Probability Question 10

#### Question 10 - 30 January - Shift 2

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 is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$. If $p: q=m$ $: n$, where $m$ and $n$ are coprime, then $m+n$ is equal to _________

## Show Answer

#### Answer: 14

#### Solution:

#### Formula: Conditional Probability, Selection of an event

$p=\frac{{ }^{6} C_1}{6 \times 6}=\frac{1}{6}$

$q=\frac{{ }^{6} C_1 \times{ }^{5} C_1 \times 4}{6 \times 6 \times 6 \times 6}=\frac{5}{54}$

$\therefore p: q=9: 5 \Rightarrow m+n=14$