Question

A pair of dice is rolled. List the elements of sample space S. Let A denote the event “the sum is less than 5” and B the event “a 6 occurs on either die”. List the elements of S corresponding to event A and to event B.

Answer 1

Rolling 2 6-sided dice, there are 36 outcomes in the sample space. You can list them, showing the result of the first die and then the result of the 2nd die, starting with (1,1) , (1,2), 1,3) etc until you get to (6,6). Event A: For the sum to be less than 5, you can have the die rolls (1,1) (1,2) (1,3) (2,1), (2,2) (3,1) so there are 6 of them where you can add the rolls together and get a sum < 5. P(A) = 6/36 = 1/6. Event B: You need a 6 on either die (or on both), so you keep the first die at 6 and run through the possibilities of the 2nd die: (6,1) (6,2) (6,3) (6,4), (6,5), (6,6). Then keep th 2nd die at 6 and go through the possiblities of the first die: (1,6) (2,6) (3,6) (4,6) (5,6) but don't list (6,6) again, we already listed it. So total there are 11 ways to get a 6 on either die or on both. To get the probability you divide 11 by the size of the sample space, so P(B) = 11/36.