Probability can be a tricky topic, but let's break it down into two easy parts: theoretical probability and experimental probability.

1. Theoretical Probability

Theoretical probability tells us what we expect to happen in an ideal situation.

Imagine flipping a fair coin.

There are two possible results: heads or tails.

So, the theoretical probability of getting heads is:

$P(\text{Heads}) = \frac{\text{Number of ways to get heads}}{\text{Total outcomes}} = \frac{1}{2}$

This means there's a 50% chance of getting heads.

2. Experimental Probability

Now, experimental probability is different.

It's based on what actually happens when we do an experiment.

Let’s say you flip that same coin 100 times.

If you get heads 45 times, the experimental probability would be:

$P(\text{Heads}) = \frac{45}{100} = 0.45$

This tells us that in this specific experiment, you got heads 45% of the time.

Recap

So, to sum it up:

• Theoretical probability is what we think will happen based on all possible outcomes.
• Experimental probability is what we find out by doing actual experiments.

Both help us understand how likely an event is, but they look at it from different angles.