A bag has 4 red and 3 black balls. A ball is drawn at random and put back into the bag together with 2 more balls of its colour. A second ball is then drawn. What is the probability that the second ball is red?

Explanation

1. 01

   First red, with probability $\frac{4}{7}$: the bag then has 6 red balls of 9. First black, with probability $\frac{3}{7}$: 4 red balls of 9.

2. 02

   $\frac{4}{7} \times \frac{6}{9} + \frac{3}{7} \times \frac{4}{9} = \frac{24 + 12}{63} = \frac{4}{7}$.