Two balls are drawn at random, one after the other with replacement, from a box containing 12 black and 9 red balls. What is the probability that the first ball is black and the second is red?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{12}{49}\)
With replacement, the first ball goes back before the second draw, so the box is the same both times and the two draws are independent. The probability of both events is the product of their probabilities.
Total balls \(=12+9=21\)
P(first black) \(\displaystyle =\frac{12}{21}=\frac{4}{7}\)
P(second red) \(\displaystyle =\frac{9}{21}=\frac{3}{7}\)
P(black, then red) \(\displaystyle =\frac{4}{7}\times\frac{3}{7}=\frac{12}{49}\)