A die is known to be biased in such a way that, when it is thrown, the probability of a six showing is. This biased die and an ordinary fair die are thrown. Find the probability that

(a) the fair die shows a six and the biased die does not show a six,

(b) at least one of the two dice shows a six,

(c) exactly one of the two dice shows a six, given that at least one of them shows a six. (C)