Question

A bag contains 10 blue marbles, 20 black marbles and 30 red marbles. A marble is drawn from the bag, its colour recorded and it is put back in the bag. This process is repeated 3 times. The probability that no two of the marbles drawn have the same colour is

• A. $\frac{1}{36}$
• B. $\frac{1}{6}$
• C. $\frac{1}{4}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{1}{6}$

No. two of the marbles drawn have some color $\Rightarrow$ we have to draw all three marbles of different colors
$\Rightarrow$ which can be done by 3 != 6 ways

So. Req. probability
$=6\times [\frac{10}{60}\times \frac{20}{60}\times \frac{30}{60}]=\frac{1}{6}$