Okay, let's break down theoretical and experimental probability. They both deal with how likely something is to happen, but they approach it from different angles.
Theoretical probability is what should happen in a perfect world. It's based on logic and math.
Experimental probability is what actually happens when you try something out in the real world. It's based on data you collect from experiments.
| Feature | Theoretical Probability | Experimental Probability |
|---|---|---|
| Definition | The probability of an event based on mathematical reasoning and assumptions. | The probability of an event based on the results of an experiment or observation. |
| Calculation | $ \text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} $ | $ \text{Experimental Probability} = \frac{\text{Number of times event occurs}}{\text{Total number of trials}} $ |
| Basis | Logic and reasoning. | Observed data. |
| Ideal vs. Reality | Represents what should happen. | Represents what actually happens. |
| Example | The theoretical probability of flipping heads on a fair coin is $\frac{1}{2}$. | If you flip a coin 100 times and get heads 53 times, the experimental probability of flipping heads is $\frac{53}{100}$. |
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