1. In my drawer I have 5 identical red socks, 3 identical blue socks and 2 identical green socks. I draw socks out of the drawer in turn and without replacement, colour unseen. Using probability trees or otherwise, evaluates the following probabilities. Show your arguments clearly.
a) I draw two socks out of the drawer. What is the probability that they are a pair (i.e. both the same colour)?
b) Suppose the first sock drawn is a red one. If I draw two more socks, what is the probability that I have a pair among the three socks?
c) Suppose the first two socks are one red and one blue. If I draw two more socks, what is the probability that I have two pairs? (10 marks)​