Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A fair coin...

Die A has 4 red and 2 white faces, whereas die B has 2 red and 4 white faces. A fair coin is flipped once. If it lands on heads, the game continues with die A; if it lands on tails, then die B is to be used.

(a) Show that the probability of red at any throw is .

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(b) If the first two throws result in red, what is the probability of red at the third throw?

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(c) If red turns up at the first two throws, what is the probability that it is die A that is being used?