Question

A bag contains $14$ balls of two colours, the number of balls of colour being equal, seven balls are drawn at random one by one. The ball in hand is returned to the bag before each new draw. The probability that at least $3$ balls of each colour are drawn, is:

• A. $\frac{1}{2}$
• B. $>\frac{1}{2}$
• C. $<\frac{1}{2}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{2}$

Total no. of balls $=14$

There are only $2$ colours of balls i.e, let them be white and black respectively.

There are $7$ white and $7$ black colour balls.

P( getting at least $3$ balls ).

At least $3$ balls means the no. of balls can be $3,4,5,6$ and $7.$

If $3$ white turns up the no. of black balls will be $4$ and vice versa.

$\therefore$ Probability of selecting a ball $=\frac{1}{2}$

P( Selecting $7$ balls ) $=\frac{7}{2}$

$\therefore$ P( getting at least $3$ balls ) $=\frac{\frac{7}{2}}{7}=\frac{1}{2}$

Hence, the answer is $\frac{1}{2}.$