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

In any trial P(getting white ball) = p(W) = 1/2P(getting black ball) = P(B) = 1/2Required event will occur if in the first six trial, 3 white balls are drawn in any of the 3 trails from six.In remaining three trails, black must be drawn.Three trials in which black balls is drawn can be selected in  6C3=20 ways.∴Required probability = P(WWWBBB in any order) x P(W)                                    =20×123×123×12=532