Experimental Probability

By the rules of probability, every time you flip a coin, you have an equal chance of getting a head or a tail. Does this mean that for every 10 times you flip the coin, you will always get 5 heads and 5 tails?

Or, by the rules of probability, every time you roll a die, you have a 1 in 6 chance of rolling a 4. Does this mean that when you roll the die 60 times, you will definitely roll a 4 ten times?

In both of these scenarios, the answer is no.

In theoretical probability, you would expect to get heads half the time and tails half the time, and in theoretical probability, you would expect to get each number of pips one-sixth of the time. But in practice, you would be unlikely to get exactly one-half heads or one-sixth 4s. Let''s say that you rolled the die 60 times and rolled a 4 a total of 8 times. In this case, the fraction

is called the experimental probability. The definition of the experimental probability of an event is the ratio of the number of favorable outcomes to the total number of trials.

With a fair die or a fair coin, you know the theoretical probability ahead of time. The more trials you conduct, the closer your experimental probability is likely to get to the theoretical probability. However, experimental probability is more helpful in situations where you don''t or can''t know the probability of the outcome ahead of time.

Examples of experimental probability

Example 1

Let''s say a basketball team has won 8 of its first 12 games. The experimental probability of its winning the next game would be:

or

Now let''s say there are 18 more games left in the season. Using experimental probability, you can predict how many of those games the team will win.



So you can probably expect that the basketball team will win 12 of the 18 games left in the season.

Example 2

Say you conduct a trial where you draw colored marbles from a bag and replace the marble each time after drawing it. After 20 trials, the following results have been noted.

• 2 – Red
  
• 5 – Blue
  
• 6 – Green
  
• 4 – Yellow
  
• 3 – Black
  

How many times can you expect a blue marble to be drawn out of 500 trials?

Since we don''t know how many total marbles or how many of each color marble are in the bag, we don''t know the theoretical probability of drawing a blue marble. However, we do know that the experimental probability of drawing a blue marble is or .

Knowing that, we can tell that the experimental probability of drawing a blue marble after 500 trials is:, or

Example 3

What about the experimental probability of drawing a yellow marble after 500 trials?

We do the same thing as we did with the blue marble. The experimental probability after 20 trials is , or . So after 500 trials, the experimental probability of drawing a yellow marble is:, or

Topics related to the Experimental Probability

Developing a Probability Distribution from Empirical Data

Probability Distribution

Probability Models

Flashcards covering the Experimental Probability

Statistics Flashcards

Probability Theory Flashcards

Practice tests covering the Experimental Probability

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

Get help learning about experimental probability

Tutoring is an excellent way to learn about experimental probability. A tutor can help your student perform actual probability trials to help them learn in a hands-on way how experimental probability works. They can also walk them through the math as many times as needed until your student gains a clear understanding of how experimental probability works. A tutor can answer your student''s questions as soon as they arise so that they learn the information correctly from the beginning.

If you''d like to learn more about how tutoring can help your student gain confidence in their understanding of experimental probability, contact Varsity Tutors today and speak with one of our helpful Educational Directors.