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
$p=\frac{{ }^{6} C_1}{6 \times 6}=\frac{1}{6}$
$q=\frac{{ }^{6} C_1 \times{ }^{5} C_1 \times 4}{6 \times 6 \times 6 \times 6}=\frac{5}{54}$
$\therefore p: q=9: 5 \Rightarrow m+n=14$
