In: Statistics and Probability
(1) Consider the random experiment where three 6-sided dice are rolled and the number that comes up (1, 2, 3, 4, 5 or 6) on each die is observed.
(a) What is the size of the sample space S of this random experiment?
(b) Find the probability of event E1: “All three numbers rolled are the same.”
(c) Find the probability of event E2: “The sum of the three numbers rolled is 5.”
(d) Find the probability of event E3: “At least one 6 is rolled.” (Hint: it may help to first find the probability of the complementary event.)