A bag contains 4 red and 6 blue balls. Three balls are drawn one by one with replacement. The probability that exactly 2 of the balls drawn are red is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{36}{125}\)
With replacement, the draws are independent and each gives a red ball with probability \(\frac{4}{10} = \frac{2}{5}\). So the number of red balls X follows a binomial distribution with
\(n = 3,\quad p = \frac{2}{5},\quad q = \frac{3}{5}\)
\( \displaystyle P(X = 2) = {}^{3}C_{2}\left(\frac{2}{5}\right)^{2}\left(\frac{3}{5}\right) \)
\( \displaystyle = 3 \times \frac{4}{25} \times \frac{3}{5} \)
\( \displaystyle = \frac{36}{125} \)