A box contains 2 black, 4 yellow and 6 white balls. Three balls are...

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?

Options

A $\frac{1}{6}$
B $\frac{1}{36}$
C $\frac{1}{12}$
D $\frac{5}{12}$

Correct answer

A. $\frac{1}{6}$

Step-by-step 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}

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