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.)

(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.

Step-by-step 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) =

                                                   =  ≅ 0.167

(c) Pr(a sum of 6 is rolled) = ≅ 0.139

(d) Pr(a sum of 11 is rolled) =

                                           = ≅ 0.056

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