Show that P(B C |A) = P(B |A) + P(C |A) if B C = . An Instant Lotto game is played with cards that have 9 windows covered with gold paint. Behind the gold paint, each game card has either an x or the picture of a prize. One of the prizes appears twice on each card, and all other prizes appear no more than once. The player rubs off the gold paint and wins if the two matching prizes are exposed before an x is exposed. Assuming that a card has x in k windows, where 0 k 7, do the following:

(a) Describe a suitable probability space {, A, P} for the experiment of playing the game.

(b) Express the event W that the player wins explicitly as a subset of . What is P(W)?