Suppose we roll a six-sided die two times.

Question

Suppose we roll a six-sided die two times.
a. List all outcomes in the sample space. (Hint: There are 36.)
b. In how many outcomes does a 6 occur at least once? List them.
c. In how many outcomes is the sum of the two rolls exactly 7? List them

Answer 1

Good Afternoon Adam!

 

a.   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

 

 

b.   11 outcomes of 6  (1-6, 2-6, 3-6, 4-6, 5-6, 6-6, 6-1, 6-2, 6-3, 6-4, 6-5)

 

 

c.    Sum of 7 outcomes-6   (1-6, 2-5, 3-4, 4-3, 5-2, 6-1)  

 

Take care and Thanks for the opportunity to serve you!  Erroll L. Franklin

Answer 2

The outcomes in your sample space are all the combinations of numbers you could get with your two rolls. For example, you could roll a 1 and then a 2, a 1 and then a 3, a 1 and then a 4, etc. You can write the 36 outcomes like this (you fill in the rest):

 

(1, 1) - 1 and then 1

(1, 2) - 1 and then 2

(1, 3) - 1 and then 3

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(3, 3) - 3 and then 3

(3, 4) - 3 and then 4

(3, 5) - 3 and then 5

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(6, 4) - 6 and then 4

(6, 5) - 6 and then 5

(6, 6) - 6 and then 6

 

Once you've listed all 36, you can simply count how many include at least one 6 and how many have a sum of 7. For example, of just the nine I listed above, three have at least one 6 in them ((6, 4), (6, 5), and (6, 6)) and one has a sum of seven ((3, 4)).