When we talk about experimental and theoretical probability, we’re looking at two key ideas that help us understand how likely events are to happen.

Theoretical Probability:

Theoretical probability is about what we expect to happen in a perfect world.

For example, think about rolling a perfect six-sided die. The theoretical probability of rolling a 3 is:

$P(3) = \frac{1}{6}$

This means that if you roll the die a lot of times, you would expect to roll a 3 about one out of every six times.

Experimental Probability:

Now, experimental probability is all about what we actually observe through experiments.

Let’s say you roll that same die 60 times and you get a 3 only 10 times. The experimental probability of rolling a 3 would be:

$P(3) = \frac{10}{60} = \frac{1}{6}$

Key Differences:

1. Basis: Theoretical probability is like a math model. It tells us what should happen. Experimental probability depends on real-life trials, showing us what actually occurs.
2. Accuracy: Theoretical probability stays the same, but experimental probability can change based on what we find in our experiments.

Real-World Scenario:

Think about flipping a coin.

Theoretically, you have a 50% chance of getting heads. But if you flip the coin 10 times and get heads 7 times, the experimental probability would be 70%.

This shows us how real-life results can be different from what we expect, and it helps us learn more about probability.