Tara has two standard, six-sided dice. If she rolls them 36 times, how many times should she expect a sum less than 5 to show up?

Justify your answer.

There are six sides on each die. For each possible score on Die 1, there are six possible scores on Die 2. So the number of possible combinations is 6*6 = 36.

It follows that if the dice are thrown 36 times, you would expect each combination to come up once.

We therefore simply need to know how many combinations add up to less than 5. (I've interpreted this as not including a total of 5 itself).

These combinations are: 1 and 1, 2 and 1, 1 and 2, 2 and 2, 3 and 1, and 1 and 3 - - - > six combinations out of 36.

So you'd expect a sum less than 5 six times.