If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Unit 8: Lesson 3

Lesson 4: Estimating probabilities through repeated experiments

# Theoretical and experimental probabilities

Compare expected probabilities to what really happens when we run experiments.

## Want to join the conversation?

• How can I tell the difference between experimental probability and theoretical probability?
• Experimental probability is the results of an experiment, let's say for the sake of an example marbles in a bag. Experimental probability would be drawing marbles out of the bag and recording the results. Theoretical probability is calculating the probability of it happening, not actually going out and experimenting. So, calculating the probability of drawing a red marble out of the bag.
• Isn't the probability still 50% but it just so happens that you got in this experiment an 80%?
(1 vote)
• That confused me too this year in seventh grade ;) As far as your question, you are totally right! Although the theoretical (expected) probability is 50%, the experimental probability doesn't have to be 50%. I like to picture a coin flip-- the theoretical probability is that the coin will land on heads once if you flip it two times, but it will not always land on heads once. Technically in your mentioned experiment, you could get any percentage even though the estimated percentage is 50%. Hope this is helpful!
• When my older brother was learning about probability, he flipped a coin to experiment, and when he flipped the coin 8 times 7/8 of the time he got tails. His teacher's reaction: "That coin is rigged."
• Sometimes that may happen. Or, to phrase that better, the chances of it happening are less, but it can still happen. If you were to flip 10 coins, you might get numbers such as 4 heads and 6 tails. But the higher the number of times you flip the coin, the closer both numbers will be to exactly half.
(1 vote)
• What would be a good definition of experimental probability?
• The experimental probability of an event is an estimate of the theoretical (or true) probability, based on performing a number of repeated independent trials of an experiment, counting the number of times the desired event occurs, and finally dividing the number of times the event occurs by the number of trials of the experiment.

For example, if a fair die is rolled 20 times and the number 6 occurs 4 times, then the experimental probability of a 6 on a given roll of the die would be 4/20=1/5. Note that the theoretical probability of a 6 on a given roll would be 1/6, since it is given that the die is fair. So experimental probability can differ from theoretical probability.

As the number of trials in the experiment grows towards infinity, the experimental probability almost surely converges towards the theoretical probability (law of large numbers).
• Are the experimental probabilities closer to the theoretical probability?
• i don't get it.did sal just mean that when the number of experiments get large experimental possibility has to be equal to the predicted number in theoretical possibility? i don't think so.
• When comparing the theoretical probabilities to your experimental probabilities. Why would there be a difference?
• I think there is a point to focus we should consider whether it is doe with or without replacement . If we ignore it then we are going to get a wrong and a vague answer . Beside that everything is okay . As the chance will be very low to get 8,000 magenta in the experiment of 10,000.
• Since there are only 100 marbles in the bag you wouldn't be able to pick 10,000 without replacement.