Question

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. $\frac{1}{2}$

Answer 1

The correct option is C $\frac{5}{32}$

Probability of drawing a white ball 4th time at 7th draw
$=($ Probability of drawing $3$ white balls in first $6$ draws$\left)\right($ Probability of drawing a white ball at the 7th draw$)$
$=\left[{}^6{C}_3{\left(\frac{1}{2}\right)}^6\right]\left(\frac{1}{2}\right)=\frac{20}{2^7}=\frac{5}{32}$