When learning about probabilities, Year 7 students often get confused between two types: theoretical probability and experimental probability. I’ve noticed this in class, so I’d like to explain some common misunderstandings.

1. Confusing Definitions

One big misunderstanding is how to define the two types of probability.

• Theoretical Probability: This is what you think will happen in a perfect situation. For example, when you flip a fair coin, you’d expect heads or tails to have a probability of $P(\text{Heads}) = \frac{1}{2}$.

• Experimental Probability: This is what really happens when you do an experiment. If you flip a coin 10 times and get heads 6 times, the experimental probability would be $P(\text{Heads}) = \frac{6}{10} = 0.6$.

Many students believe these two probabilities should always be the same, but that’s not true!

2. Misunderstanding Results

Another common mistake is thinking experimental results should always match the theoretical probabilities. It's important for students to realize that because of randomness, results can change a lot.

• For example, if you roll a six-sided die 30 times and get the number 3 only 2 times, the experimental probability would be $P(3) = \frac{2}{30} = \frac{1}{15}$. This doesn’t mean the theoretical probability is wrong; it still is $P(3) = \frac{1}{6}$.

3. Believing in "Due" Outcomes

Another idea students sometimes believe is that outcomes are “due” to happen. They think if something hasn’t happened in a while, it’s time for it to occur.

• For example, if a coin lands on heads 5 times in a row, they might think tails is more likely to happen next. In reality, each flip is independent, and the theoretical probability stays $P(\text{Tails}) = \frac{1}{2}$, no matter what happened before.

4. Ignoring Sample Size

Students often forget how the number of tries can change the reliability of experimental probability. Smaller sample sizes can lead to big differences from the theoretical probability.

• For example, if you flip a coin 10 times and get 7 heads, you might think the probability of heads is higher. But if you flip the coin 1000 times, the probabilities usually come closer to what you expect theoretically.

5. Misunderstanding Probability

Finally, students sometimes misinterpret what probability tells us. For example, they may think that a probability of $0.9$ means the event will happen 9 times out of 10 trials. Instead, it just shows that there’s a high chance of that outcome happening, not a promise that it will happen that many times.

To help students, it's great to use hands-on experiments that show both theoretical and experimental probability. Using real-life examples like games or sports can make these ideas easier to understand. When they see the differences and learn to welcome randomness, they will find probability more fun and easier to grasp!