Question

24.Rolling Die Two dice are rolled. Find the probability of getting

a.A sum of 8, 9, or 10

b.Doubles or a sum of 7

c.A sum greater than 9 or less than 4

d.Based on the answers to a, b, and c, which is least likely to occur?

Answer 1

When Two dice are rolled:

Total number of events = 6x6 = 36

a.

Probability of getting sum of 8, 9, or 10:

Following are the events that favor sum 8,9 or 10:

Dice 1	Dice 2	Sum
2	6	8
3	5	8
4	4	8
5	3	8
6	2	8
3	6	9
4	5	9
5	4	9
6	3	9
4	6	10
5	5	10
6	4	10

Number of events that favor of getting sum of 8,9 or 10 = 12

Probability of getting sum of 8, 9, or 10

= Number of events that favor of getting sum of 8,9 or 10 / Total number of events = 12/36=1/3

Probability of getting sum of 8, 9, or 10 =1/3 = 0.3333

b. Probability of getting Doubles or a sum of 7

Events that favor doubles or a sum of 7

Dice 1	Dice 2	Sum
1	6	7
2	5	7
3	4	7
4	3	7
5	2	7
6	1	7
1	1	Double
2	2	Double
3	3	Double
4	4	Double
5	5	Double
6	6	Double

Number of events that favor doubles or a sum of 7 =12

Probability of getting Doubles or a sum of 7

= Number of events that favor doubles or a sum of 7 / Total number of events =12/36 = 0.3333

Probability of getting Doubles or a sum of 7 = 1/3 =0.3333

c. Probability of getting A sum greater than 9 or less than 4

Event that favor getting A sum greater than 9 or less than 4

Dice 1	Dice 2	Sum
1	1	2
1	2	3
2	1	3
4	6	10
5	5	10
6	4	10
5	6	11
6	5	11
6	6	12

Number of events that favor getting a sum greater than 9 or less than 4 = 9

Probability of getting A sum greater than 9 or less than 4

= Number of events that favor getting a sum greater than 9 or less than 4 / Total number of events = 9/36 = 1/4 = 0.25

Probability of getting A sum greater than 9 or less than 4 =1/4 = 0.25

d.

a. Probability of getting sum of 8, 9, or 10 = 0.3333

b. Probability of getting Doubles or a sum of 7 = 0.3333

c. Probability of getting A sum greater than 9 or less than 4 = 0.25

As c. Probability of getting A sum greater than 9 or less than 4 = 0.25 which is the least among the three events, hence 'c' is least likely to occur.