Using the 36 possibilities found in the product table for ro

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice) is the following. Less than 4 Which is correct below?

(1,1), (1,2); 2

(1,1), (1,2), (2,1); 3

(1,1), (2,2), (1,2), (2,1); 4

(1,1), (1,2), (2,1), (1,3), (3,1), (2,2); 6

Solution

If we roll the die, looking for sums of less than four we can easily list out the rolls counting up to three since it is a low number and most of the 36 possibilities will be above 4.

We start with rolling a 1.

(1,1) (1,2)

If we rolled a (1,3) then that would be 4 and not under 4 so we stop there.

Then we roll with a 2.

(2,1)

If we roll (2,2) that is four as well and not under 4 so we stop there.

There are no more possibilities to roll that sums are not under 4.

There are 3 possibilities for rolling a sum from both die under 4.

THE ANSWER FOR LESS THAN 4 IS

(1,1), (1,2), (2,1); 3