When we explore the topic of probability, two important ideas come up: theoretical probability and experimental probability.

Both of these concepts help us understand how likely something is to happen, but they use different methods to do so.

Theoretical Probability
This is all about what could happen based on all possible results.

You can figure it out using this formula:

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

For example, if you roll a fair six-sided die, the chance of rolling a 3 is:

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

This is because there’s one way to roll a 3 out of six possible options (1, 2, 3, 4, 5, 6).

Experimental Probability
In contrast, experimental probability comes from doing real-life trials. It looks at how many times something actually happens compared to how many times you tried. The formula is:

$P(E) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}$

Let’s say you roll the die 30 times and you get a 3 five times. You would find the experimental probability like this:

$P(3) = \frac{5}{30} = \frac{1}{6}$

This result matches our theoretical probability, but sometimes they can be different!

Summary

• Theoretical Probability: What should happen based on possible outcomes.
• Experimental Probability: What actually happened based on real trials.

Both of these ideas help us understand probability better, allowing us to make predictions and analyze different situations!