Kamila has two number cubes each labeled 1 to 6. she is going to conduct an experiment by tossing both cubes a total of 150 times. she will find the sum numbers in each roll. how many possible outcomes are there?

Given that Kamila is tossing two number cubes 150 times. And then adds the result of both cubes in each toss.

Now we have to find possible number of outcomes.

Let's consider first toss:

First die can result in any of 1,2,3,4,5 or 6.

Second die can result in any of 1,2,3,4,5 or 6.

Now if we combine them to make possible outcomes then we will get total 36 different combination (as shown in attached picture) which is just 6 times 6 results of both dice.

For all 150 tosses, we will get any one of those 36 listed outcomes.

We are looking for sum of numbers on both dices so we get:

{2,3,4,5,6,7,8,9,10,11,12}

From the table we can see that there are only 11 different possible outcomes.

So answer will be:

Total number of possible different sums = 11

Total number of possible combination of numbers from each dice = 36