A ball is drawn from an urn containing 3 white and 3 black b

A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is then replaced and another ball is drawn. This goes on indefinitely. What is the probability that the first white ball appears in the 10th draw?

A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is then replaced and another ball is drawn. This goes on indefinitely. What is the probability that the first white ball appears in the 10th draw?

Solution

Let

W, B = white, black

As

P(W) = 3/6 = 0.5
P(B) = 3/6 = 0.5

Hence,

P(BBBBBBBBBW) = 0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5*0.5* = 0.000976563 [ANSWER]