What is the difference between theoretical and experimental probability?

Answer

Theoretical probability is what should happen based on mathematical reasoning, while experimental probability is what actually happens when you conduct trials or experiments.

Theoretical probability is calculated using logic and mathematical formulas. For example, if you flip a fair coin, the theoretical probability of getting heads is 1/2 (or 50%) because there are two equally likely outcomes and heads is one of them. You determine this without actually flipping the coin.

Experimental probability is based on real observations and data. If you flip a coin 100 times and get heads 47 times, the experimental probability of heads is 47/100 (or 47%). This comes from what you actually observed during the experiment.

The key differences:

• Calculation method: Theoretical uses mathematical reasoning; experimental uses collected data
• Basis: Theoretical is based on what's expected; experimental is based on what occurred
• Variability: Theoretical probability stays constant; experimental probability can vary each time you run the experiment
• Sample size effect: Theoretical probability doesn't change with more trials, but experimental probability typically gets closer to theoretical probability as you increase the number of trials (this is called the Law of Large Numbers)

For instance, if you roll a standard die, the theoretical probability of rolling a 3 is 1/6. But if you roll it 30 times, you might only get a 3 four times, giving you an experimental probability of 4/30. Roll it 1,000 times, and your experimental probability will likely be much closer to that theoretical 1/6.

Yes · 0 No · 0 Add Comment · 0

Add ·

Report