Question

When two six-sided dice are rolled, there are 36 possible outcomes.

Find the probability that the sum is not 4.

Find the probability that the sum is greater than 5.

Answer 1

33/36 ; 26/36

Explanation:

A) To find the probability that the sum is not four, let's discover how many sums do equal four.

1. 1+3=4
2. 3+1=4
3. 2+2=4

There are three possibilities that the sum is four. So:

36-3=33 possibilities where the sum is not four. Or,
`(33)/(36)` in probability terms.

B) Similarly, lets find out how many possibilities would be greater than five. However, to make it quicker, let's do the opposite, and then subtract. We already know how many equal four. Now: how many possibilities result in a sum of 2, 3, or 5?

1. 1+1=2
2. 1+2=3
3. 2+1=3
4. 1+4=5
5. 4+1=5
6. 2+3=5
7. 3+2=5

Including the sums of four we found earlier, this leaves 10 possible outcomes where the sum is less than or equal to five. Or, in other words, 26 possible outcomes where the sum is greater than five.

`(26)/(36)`, in probability terms.