Question

Consider a die with only 4 sides, marked 3, 6, 9, and 12. A pair of these dice is rolled.

1. Make a table to show the sample space for the roll.

	3	6	9	12
3
6
9
12

2. What is the probability that the sum of the dice is 18?

Answer 1

we consider a die with only 4 sides, marked 3, 6, 9 and 12.

A pair of such dice are rolled.

(a)

To find the sample space for this roll.

The sample space is shown in the table.

	3	6	9	12
3	(3,3)	(3,6)	(3,9)	(3,12)
6	(6,3)	(6,6)	(6,9)	(6,12)
9	(9,3)	(9,6)	(9,9)	(9,12)
12	(12,3)	(12,6)	(12,9)	(12,12)

So, the events in the sample space are those shown in the table.

(b)

To find the probability that the sum of the dice is 18.

Now, the first dice can have 4 outcomes, and so can the second dice, independently.

So, the number of all possible cases is

4*4, ie. 16.

Now, the sum of the two dice can be 18, in only these ways.

(6,12), (9,9), and (12,6).

So, there are 3 favourable cases only.

So, the probability is

3/16.

So, the required answer is 3/16.