Question

A bag contains three white, two black and four red balls. If four balls are drawn at random with replacement, the probability that the sample contains just one white ball is

• A. $\frac{32}{81}$
• B. $\frac{11}{2}$
• C. $\frac{32}{93}$
• D. None of these

Answer 1

The correct option is A $\frac{32}{81}$

The probability $p$ of getting w white ball in a single draw is $\frac{3}{9}=\frac{1}{3}$,
If $X$ is the number of white balls drawn, then $X\sim B(n,p)$, with $n=4$.
Therefore the probability of getting exactly one white ball is
$P(X=1){=}^4{C}_{1}p{q}^3=4\left(\frac{1}{3}\right){\left(\frac{2}{3}\right)}^3=\frac{32}{81}$