Consider an experiment where two 6-sided dice are rolled. We can describe the or
ID: 3297676 • Letter: C
Question
Consider an experiment where two 6-sided dice are rolled. We can describe the ordered sample space as below where the first coordinate of the ordered pair represents the first die and the second coordinate represents the second die. S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1) (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} (a) Describe the event E that the sum of the two dice is 5. (b) Describe the event F that the number of the first die is exactly 1 more than the number on the second die. (c) If the dice are 'fair', are all 36 of these possible outcomes equally likely?Explanation / Answer
a) Event E: The sum of the two dice is 5,which means that sum of the numbers obtained in 1st die and 2nd die is 5.
So outcomes favourable are: (1,4) (2,3) (3,2) (4,1) where the sum of the two co-ordinates is 5. So no of favourable events is 4. If we need the probability of this event then it is = 4/36 or 1/9.
b)Event F: The number on the first die is exactly 1 more than the number on the second die.
So outcomes favourable are:(2,1) (3,2) (4,3) (5,4) (6,5)
So no of favourable outcomes are 5. So the corresponding probability is 5/36.
c) yes. if the dice are fair,then chance of each of the 6 faces to appear is 1/6 and hence all of the 36 of these possible outcomes are equally likely.