Question

If two dice are rolled one time, find the probability of getting these results. Show all possible combinations. Express the probability as a fraction of 36

A 3 on one die or on both dice
A sum greater than or equal to 10

Answer 1

Explanation:

any particular result with 2 dice has a probability of

1/6 × 1/6 = 1/36

a 3 on one die or both simply means at least one 3.

so, if all the 36 different outcomes we are looking at

3 1

3 2

3 3

3 4

3 5

3 6

1 3

2 3

4 3

5 3

6 3

the 3 3 combination can be counted only once !

so, we have 11 desired outcomes out of the possible 36.

so, the probability of getting at least one 3 is

11/36

the sum of at least 10 means the corresponding cases

4 6

5 5

5 6

6 4

6 5

6 6

in this case we don't need to turn this around, because it would be exactly the same outcomes again, and we don't want to count them twice.

so, we have 6 desired outcomes of the 36.

the probability of that is

6/36 = 1/6