A bag contains two red balls and three blue balls. Two balls are drawn at random, one after the other without replacement, and their colours are recorded. Both balls are then returned to the bag.
This procedure is repeated independently, giving two more recorded colours. At each draw, every ball then in the bag is equally likely to be chosen.
Given that the four recorded colours consist of two reds and two blues, what is the probability that each pair drawn contained one ball of each colour?
A
B
C
D
E