A box contains 24 identical balls of which 12 are white and 12 black. The balls

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A box contains 24 identical balls of which 12 are white and 12 black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the

4^{t h}

time on the

7^{t h}

draw is

Options:

A . 564

B . 2732

C . 532

D . 12

Answer: Option C
:
C
In any trail, P(getting white ball) =

\frac{1}{2}

P(getting black ball) =

\frac{1}{2}

Now, required event will occur if in the first six trails 3 white balls are drawn in any one of the 3 trails from six. The remaining 3 trails must be kept reserved for black balls. This can happen
In

^{6} C_{3} \times^{3} C_{3} = 20

ways.

= 20 \times {(\frac{1}{2})}^{3} \times {(\frac{1}{2})}^{3} \times \frac{1}{2} = \frac{5}{32}

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