There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white, is
Answer & explanation
Correct answer: option 2
We have,
p = probability of getting a white ball in a draw $=\frac{1}{2}$
q = probability of getting a red ball in a draw $=\frac{1}{2}$
Getting 4th white ball in 7th draw means that, we must get 3 white balls in first six draws and a white ball in 7th draw.
∴ Required probability $= \begin{Bmatrix}{^6C}_3 \left(\frac{1}{2}\right)^3\left(\frac{1}{2}\right)^{6-3}\end{Bmatrix} \frac{1}{2}=\frac{5}{32}$