Study Curve

Probability is defined by the opportunity to for something to happen. In this case how likely is it that you will roll a certain number(s) out of 12 opportunities. The simplest way to think of this is how many chances do I have to achieve a goal of the total opportunities. Specifically, in this example you have a total of 12 opportunities (12 sided die).

a.) Prime numbers are those that are greater than one and can only be divided by 1 or itself. So in this case the prime numbers greater than one and less than or equal to 12 are: 2, 3, 5, 7, 11 so the probability of rolling one of these numbers is 5 in 12 or 5/12 or .416 or 41.6% because there are 5 numbers you could roll out of a total opportunity of 12.

b.) Composite numbers are the opposite of prime numbers by definition, they have to be divisible by a number that is not equal to one and itself. In this case the composite numbers are: 4, 6, 8, 9, 10 and 12 so the probability of rolling a composite number is 6 out of 12 or 6/12 or .5 or 50%.

C.) Finally, the probability of rolling neither a prime or composite number is the remaining which is the number 1 so you have the lowest probability in this scenario of 1 in 12 or 1/12 or .083 or 8.3%.

Hope this helps!