A box contains 24 identical balls of which 12 are white and 12 are 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 4th time on the 7th draw is `5//64` b. `27//32` c. `5//32` d. `1//2`

Options

A. `5//64`
B. `27//32`
C. `5//32`
D. `1//2`

Answer

C

Explanation

In any trial P (getting white ball) = P (W) =1/2
P(getting black ball)`=P(B)=1//2`
Required event will occur if in the first six trial, 3 white balls are drawn in any of the 3 trials from six.
In remaining three trials, black must be drawn. Three trials in which black balls is drawn can be selected in `""^(6)C_(3)=20` ways.
`therefore"Required probability"=P(WWWWBBB"in any order")xxP(W)`
`=20xx((1)/(2))^(3)xx((1)/(2))^(3)xx1/2=5/32`