Chuck-a -luck " is played by simultaneously rolling 3 dice.

a)Describe the sample space S; how many sample points are there? Justify your answers.

b) Let P be the equally likely probability measure on S. Let B denote the probability that the numbers on the 3 dice are different. Compute P (B) =

c)Let Ai denote the event that the number 6 appears i times, where i = 0, 1, 2, 3.Compute :

(i)P (A0) = (ii)P (A1) = (ii)P (A2) = (iv)P (A3) =

c) Are the events Ai and B pairwise disjoint? pairwise independent? [ hint :calculate P (Ai B) for i = 0, 1, 2, 3.]

d) Are the events Ai and B are mutually independent?