Rolling Two DiceWhen two dice are rolled, find the probability of getting

a. A sum of 5 or 6

b. A sum greater than 9

c. A sum less than 4 or greater than 9

d. A sum that is divisible by 4

e. A sum of 14

f. A sum less than 13 (4–1)

Solution 6RE

Step1 of 7:

From the given problem we have two fair dice. We know that a fair die has 6 faces that is

{1, 2, 3, 4, 5, 6}. Then, the total number of outcomes is = 36.

Here our goal is:

a). We need to find the probability of a sum of 5 or 6.

b). We need to find the probability of a sum greater than 9.

c). We need to find the probability of a sum less than 4 or greater than 9.

d). We need to find the probability of a sum that is divisible by 4.

e). We need to find the probability of a sum of 14.

f). We need to find the probability of a sum less than 13.

The possible number of outcomes are:

{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (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)}

Step2 of 7:

a).

The possible number of outcomes that have sum 5 is:

{(1,4), (2,3), (3,2), (4,1)}

Similarly, The possible number of outcomes that have sum 6 is:

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

Then, The probability of a sum of 5 or 6 is:

Therefore, The probability of a sum of 5 or 6 is 0.2499.

Step3 of 7:

b).

The probability of a sum greater than 9 is:

Therefore, The probability of a sum greater than 9 is

Step4 of 7:

c).

The probability of a sum less than 4 or greater than 9 is:

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