At the ninth hole on a certain golf course there is a pond. A golfer hits a grade B ball into the pond. Including the golfer's ball there are then six grade C, ten grade B and four grade A balls in the pond. The golfer uses a fishing net and 'catches' four balls. The events X, Y and Z are defined as follows: X: the catch consists of two grade A balls and two grade C balls Y: the catch consists of two grade B balls and two other balls Z: the catch includes the golfer's own ball Assuming that the catch is a random selection from the balls in the pond, determine

(a) P(X),

(b) P(Y),

(c) P(Z),

(d) P(Z|Y). For each of the pairs X and Y, Y and Z, state, with a brief reason, whether the two events are (i) mutually exclusive, (ii) independent.