Theoretical probability

The theoretical probability is found whenever you make use of a formula to find the probability of an event.

To find the probability of an event, also called likelihood of an event, use the formula below:

probability of an event =
number of favorable outcomes / number of possible outcomes


The number of favorable outcomes is the likelihood to get a specific outcome.

What about the number of possible outcomes? Suppose you throw a die numbered from 1 to 6.

Count all the possible numbers you can get. This is called number of possible outcomes.

All the possible numbers are 1, 2, 3, 4, 5, and 6. Thus the number of possible outcomes is 6.

You could make up different types of favorable outcomes.

You could say...

a. Likelihood to get an even number.

b. Likelihood to get a prime number.

c. Likelihood to get an odd number.

d. Likelihood to get a 4.

e. Likelihood to get a 1.

f. Likelihood to get a number bigger than 4.

g. Likelihood to get a number less than 6.

All the above are examples of favorable outcomes.

A couple of examples showing how to find the theoretical probability.

Theoretical probability versus experimental probability

Exercise #1

Throw a die once. What is the probability of getting a number less than 6?

Ask yourself, "How many number are less than 6?"

Since there are 5 numbers less than 6, the number of favorable outcomes is 5.

Since the die had a total of 6 numbers, the number of possible outcomes is 6.

probability of getting a number less than 6 =
number of favorable outcomes / number of possible outcomes


probability of getting a number less than 6 =
5 / 6


probability of getting a number less than 6 = 0.8333.

probability of getting a number less than 6 = 83.33%

This means that it is very likely you will get a number less than 6.


Exercise #2

A bag contains 6 blue balls, 4 yellow balls, and 2 red balls.

What is the theoretical probability of getting a yellow ball?

Since you have 4 yellow balls playing on your favor, the number of favorable outcomes is 4.

To get the number of possible outcomes, just count all the balls. Number of possible outcomes is 12.

probability of getting a yellow ball =
4 / 12


probability of getting a yellow ball = 0.3333

probability of getting a yellow ball = 33.33%

Theoretical probability quiz. How good are you?

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