Question

1. Find the probability of rolling a sum less than 4 or a
sum greater than 8 when a pair of dice is rolled.

Answer 1

Answer:  13/36

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Explanation:

Refer to the chart below. The values in red up top add to the values in blue along the left column to get the 6 by 6 grid of values inside. This represents all of the possible ways to add up values on a pair of dice. There are 6*6 = 36 outcomes.

Of those 36 outcomes, we have 13 outcomes where we roll less than a 4, or greater than 8

1. outcome = 1+1 = 2
2. outcome = 1+2 = 3
3. outcome = 2+1 = 3
4. outcome = 3+6 = 9
5. outcome = 4+5 = 9
6. outcome = 5+4 = 9
7. outcome = 6+3 = 9
8. outcome = 4+6 = 10
9. outcome = 5+5 = 10
10. outcome = 6+4 = 10
11. outcome = 5+6 = 11
12. outcome = 6+5 = 11
13. outcome = 6+6 = 12

These 13 results are shown in green boxes in the diagram.

Since we have 13 ways to get what we want, out of 36 total, the final answer as a fraction is therefore 13/36

13/36 = 0.3611 = 36.11% approximately