Question

A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?

Answer 1

Let X denote the number of red balls drawn from 16 balls with replacement.
X follows a binomial distribution with n = 4, 

\[p = \frac{5}{16}, q = 1 - p = \frac{11}{16}\]

\[P(X = r) = ^{4}{}{C}_r \left( \frac{5}{16} \right)^r \left( \frac{11}{16} \right)^{4 - r} \]
\[P(\text{ One ball is red } ) = P(X = 1) \]
\[ = ^{4}{}{C}_1 \left( \frac{5}{16} \right)^1 \left( \frac{11}{16} \right)^{4 - 1} \]
\[ = 4\left( \frac{5}{16} \right) \left( \frac{11}{16} \right)^3 \]
\[ = \frac{5}{4} \left( \frac{11}{16} \right)^3\]