A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?

• Correct answer
  A

  $\frac{1}{6}$
• B

  $\frac{1}{36}$
• C

  $\frac{1}{12}$
• D

  $\frac{5}{12}$

Solution

To get all 3 balls of same colour, ball drawn must be either yellow or white with replacement. Required probability $\begin{aligned} & =\frac{2}{12} \times \frac{2}{12} \times \frac{2}{12}+\frac{4}{12} \times \frac{4}{12} \times \frac{4}{12}+\frac{6}{12} \times \frac{6}{12} \times \frac{6}{12} \\ & =\frac{8}{1728}+\frac{64}{1728}+\frac{216}{1728}=\frac{288}{1728}=\frac{1}{6} \end{aligned}$

Hence, the correct answer is option: 'A'.