A manufacturer of glass marbles produces equal large numbers of red and blue marbles. These are thoroughly mixed together and then packed in packets of six marbles which are random samples from the mixture. Two boys, Tom and Vusi, each buy a packet of marbles. Tom prefers the red ones and Vusi the 2 blue ones, so they agree to exchange marbles as far as possible, in order that at least one of them will have six of the colour he prefers. Find the probabilities that, after exchange: (a) They will both have a set of six of the colour they prefer. (b) Tom will have four or more blue ones.