Question

You roll two, fair (i.e., not weighted) 6-sided dice once. What is the probability that: 3a. The sum is 11 or more? (1 Point)

3b. The sum is 7? (1 Point)

3c. The sum is 6? (1 Point)

3d. Thesumis6or8? (1Point)

3e. The sum is less than 4? (1 Point)

3f. The sum is something other than 2, 7, or 11? (2 Points)

Answer 1

when you roll two dice , all possible events are:

(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)

Hence

Total(n(S))=36

3a. The sum is 11 or more?

Events that have 11 or more?=(5,6),(6,5)

No. of events(n(S))=2

Required Probability=2/36=1/18

3b. The sum is 7? (1 Point)

Events that have 7?=(1,6),(2,5), (3,4),(4,3),(5,2),(6,1)

No. of events(n(S))=6

Required Probability=6/36=1/6

3c. The sum is 6?

Events that have 6?=(1,5),(2,4),(3,3),(4,2),(5,1)

No. of events(n(S))=5

Required Probability=5/36

3d. The sum is 6 or 8?

Events that have 6 r 8?=(1,5),(2,4),(3,3),(4,2),(5,1), (2,6),(3,5),(4,4),(5,3), (6,2)

No. of events(n(S))=10

Required Probability=10/36=5/18

3e. The sum is less than 4?

Events that sum is less than 4?=(1,1), (1,2),(2,1)

No. of events(n(S))=3

Required Probability=3/36=1/12

3f. The sum is something other than 2, 7, or 11?

Events that sum is something other than 2, 7, or 11=

(1,2),(1,3),(1,4),(1,5),

(2,1), (2,2),(2,3),(2,4),(2,6),

(3,1), (3,2),(3,3),(3,5),(3,6),

(4,1), (4,2),(4,4),(4,5),(4,6),

(5,1), (5,3),(5,4),(5,5),

(6,1), (6,2),(6,3),(6,4),(6,6)

No. of events(n(S))=28

Required Probability=28/36=7/9