When we talk about probability, especially for 7th graders, it's really important to understand the difference between two types: theoretical probability and experimental probability. Let’s make this simple and clear.

Theoretical Probability:

1. What It Is: This is what we think will happen in a perfect situation. It’s based on all the possible results of an event.

2. How to Calculate It: You can find it using this formula: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

   For example, if you roll a regular 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 and six total options (1, 2, 3, 4, 5, 6).

3. Predicting Outcomes: Theoretical probability helps us guess what should happen before we actually do an experiment. It’s like making an educated guess based on everything we know.

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Experimental Probability:

1. What It Is: This is what really happens when you do the experiment. It’s based on the results you get from trials.

2. How to Calculate It: You find this using the formula: $P(A) = \frac{\text{Number of times event A happens}}{\text{Total number of trials}}$

   So, if you rolled the die 30 times and got a 3 five times, the experimental probability of rolling a 3 would be: $P(3) = \frac{5}{30} = \frac{1}{6}$

   This might be surprising, but it matches the theoretical probability! Just remember, this doesn’t always happen.

3. Real-World Results: Experimental probability shows what really happens and can change. It’s like doing an experiment at school, where your results might be different from what you expected because of luck, mistakes, or other limits.

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Important Points to Remember:

• Theoretical probability is focused on what could happen, while experimental probability shows what actually happened after trials.

• After many trials, experimental probability often matches with theoretical probability, but it won’t always do so! This is a fun way to show that math can be full of surprises.

Understanding both types of probability gives you a strong base in math. This makes it easier to learn more complex ideas later. Keep practicing, and you’ll see how everything connects!