Q. 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
A) $\frac{5}{64}$
B) $\frac{27}{32}$
C) $\frac{5}{32}$
D) $\frac{1}{2}$
Explanation
(c)
Probability of getting a white ball at any draw is, $p$
$= \frac{12}{24} = \frac{1}{2}$.
The probability of getting a white ball $4th$ in the 7$th$ draw
$= P$ (getting 3 white balls in 6 draws)$\times P$ (white ball at the 7$th$ draw)
$= {\ ^{6}C}_{3}\left( \frac{1}{2} \right)^{6} \bullet \frac{1}{2} = \frac{20}{2^{7}} = \frac{5}{32}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.