Theoretical probability is the probability that comes from the perfect distribution. If you roll a die, the odds of a value of 1-3 is 50%, *exactly*.

Experimental probability is the *observed* probability distribution for a given set of attempts. For example, if you rolled a die 10 times, and 6 of them were 1-3, then that same *experimental* probability is 60%.

If you repeat an experiment enough times, the experimental probability should converge onto the theoretical probability. If it doesn’t, the theoretical probability doesn’t actually describe the situation you are looking at. Regardless, the core difference is, theoretical is an abstract value that exists *completely separate* from the outcome (10 heads in a row won’t change a 50% chance), while the experimental is based entirely on evaluating the observed outcomes and describing the underlying probability there from.

Theoretical probability is like guessing the chances of something happening using math. It’s like predicting if your favorite team will win based on stats. Experimental is when you actually do something to find out, like flipping a coin tons of times to see how often it lands on heads. Hope that helps!

The theoretical probability is the mathematical odds.

A coin flip has 50/50 odds, mathematically.

So then you do the experiment and flip a US nickel 10,000 times, recording 5,127 heads and 4,873 tails.

Your measured experimental probability isn’t 50/50, it’s 51/49.

Maybe the nickel is actually slightly unbalanced. Maybe you flip it with a bias. Maybe this is just random variability. If your experimentally measured probability is way different than the theoretical probability, you have to try to explain why. Either the theory is wrong or your experiment was flawed.

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