WAEC Mathematics 2012 Paper

Concept:For two draws without replacement, the probability of different colours is the sum of the probability of red then black and black then red.Explanation:Total balls in the bag: $4 + 6 = 10$.Probability that the first ball is red: $\frac{4}{10}$.After one red ball is removed, 9 balls remain, of which 6 are black.So $P(\text{red then black}) = \frac{4}{10} \times \frac{6}{9} = \frac{24}{90}$.Probability that the first ball is black: $\frac{6}{10}$.After one black ball is removed, 9 balls remain, of which 4 are red.So $P(\text{black then red}) = \frac{6}{10} \times \frac{4}{9} = \frac{24}{90}$.Therefore, total probability of different colours is:$$P = \frac{24}{90} + \frac{24}{90} = \frac{48}{90} = \frac{8}{15}$$Answer:$\frac{8}{15}$ Correct option: A. $\;\frac{8}{15}$