If Two dice are rolled Find the probability of getting a sum greater than 8?

Answer 1

The first die can be from 2 to 6, it can not be one. So, the first die has a 5/6 chance. The second die must be a 2 if 6 is on the first die, 3 if 5 is on the first die, etc. so it has a 1/6 chance. Since the two events must occur ("and" situation) and they are independent:

(1/6) * 5/6 = 5/36.

A second way of thinking about this is, that each die can have values from 1 to 6, so you can make a x-y table (1-6 columns and 1-6 rows) and see 36 combinations, of which only 5 will add to 8:

(2,6) (6,2) (3,5) (5,3) (4,4)

so the answer is 5/36.

We know that there are 36 different possible dice rolls.

Since the dice must be greater than 8, we have the following combinations:

3-6 x2

4-5 x2

4-6 x2

5-5

5-6 x2

6-6

Which is 10, or 5/18.

If you looking for > or = to 8, we must add:

2-6 x2

3-5 x2

4-4 to this list.

Which is 15 => 5/12