Question

12.5.17

Two dice are rolled.

a) Determine the number of points in the sample space.

b) Determine the probability that a double (a 1, 1 or 2, 2, etc.) is rolled.

c) Determine the probability that a sum of 6 is rolled.

d) Determine the probability that a sum of 11 is rolled.

e) Are you as likely to roll a sum of 6 as you are of rolling a sum of 11?

a) There are 36 points in the sample space.

b) The probability that a double is rolled is

(Simplify your answer.)

Answer 1

(a) 36 points

(b) Pr(rolling a double number) ≅ 0.167

(c) Pr(a sum of 6 is rolled) ≅ 0.139

(d) Pr(a sum of 11 is rolled) ≅ 0.056

(e) No.

Explanation:

Sample space = {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) The number of points in the sample space is 36.

(b) Pr(rolling a double number) =
`(6)/(36)`

=
`(1)/(6)` ≅ 0.167

(c) Pr(a sum of 6 is rolled) =
`(5)/(36)` ≅ 0.139

(d) Pr(a sum of 11 is rolled) =
`(2)/(36)`

=
`(1)/(18)` ≅ 0.056

(e) No. It is more likely to roll a sum of 6 than that a sum of 11.