What is theoretical probability?

Theoretical probability is the probability of an event based on a theory or guess of what you would expect to happen.

For example, when flipping a fair coin you would expect it to be heads half of the time and tails the other half of the time. This would be written as:

1/2 or 0.5 or 50%

Example 1:

What is the theoretical probability of getting heads when flipping a fair coin 10 times?

Since it is a fair coin, I know there is an equal chance of getting heads and tails.

So, I would expect to get 5 heads

The theoretical probability would be 5/10 or 1/2.

What if I flipped the same coin 100 times?  What is the probability of getting heads?

Example 2:

What is the theoretical probability of rolling a 3, when I roll one 6-sided die?

I know there is only 1 way to get a 3 and there are 6 total options.

So, the probability of rolling a 3 is 1/6.

What is the theoretical probability of rolling  a 5, when I roll one 6-sided die?

Probability of rolling a 5 = (The total # of 5's on the die)/(The total number of options)

So, P(5) = 1/6

P(5) means the Probability of rolling a 5, it is just a shorter way to write it.  You will see this notation a lot as you explore probability further.

If you are ready to test your knowledge of Theoretical probability,