Theoretical probability is the probability that an event occurs when all of the outcomes of the experiment are equally likely.
Theoretical Probability

number of ways the event can occur
number of ways the event can occur P(event) = _____________________________________
total number of equally likely outcome

A bag contains 6 red marbles and 12 blue ones. You select one marble at random from the bag.

(1)What is the probability that you select a red marble? Write your answer in the simplest form

(2) What is the probability that you select a blue marble? Write your answer in the simplest form

We found this out by taking the amount of red marbles there are and the total amount of marbles. The total amount of marbles is 18 and there are red marbles. So, it would become 6 out of 18 or 6/18. Then, we simplify 6/18 to the simplest form. The greatest common factor of both of those numbers is 6. Lastly, we divide each of them by 6 to get the simplest form.

6/18 = (6/6)/(18/6)

(6/6)/(18/6) = 1/3

So, therefore, the theoretical probability of picking a red marble is 1/3.

2. The probability that we select a blue marble is 2/3.

We can find this out by taking the amount of blue marbles there are and the total amount of marbles. We know that the total amount of marble is 18 and there are 12 blue marbles. So, we simply get the GCF (greatest common factor) and divide them by it.

Greatest Common Factor of 12 and 18 = 6

12/18 = (12/6)/(18/6)

(12/6)/(18/6) = 2/3

Thus, the theoretical probability of picking a blue marble is 2/3.