Calculating the chances of simple events is an important part of math, especially in Year 10.

Probability helps us understand how likely something is to happen. We usually show this as a number between 0 and 1 or as a percentage.

Theoretical Probability

Theoretical probability uses a formula to find the chance of an event:

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

For example, let’s say you roll a fair six-sided die and want to know the chance of rolling a 3.

• You have one favorable outcome (rolling a 3).
• And six possible outcomes (1 through 6).

So, the probability of rolling a 3 is:

$$P(3) = \frac{1}{6} \approx 0.17 \text{ or } 17\%$$

Experimental Probability

Now, let’s talk about experimental probability. This is based on real-life experiments or trials. You can calculate it like this:

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

For instance, if you roll the die 60 times and get a 3 twelve times, the experimental probability would be:

$$P(3) = \frac{12}{60} = \frac{1}{5} = 0.2 \text{ or } 20\%$$

By learning about both theoretical and experimental probability, you can better analyze and predict outcomes in different situations!