# Experimental and Expected Frequencies

Lesson

We have already learned about probability which is the chance of an event occurring. However, if you have ever done a probability activity in class, you may have noticed that what you expected to happen was different to what actually happened. In maths, we call this the expected frequency and the experimental (or observed) frequency. Remember frequency means how often an event occurs.

## Expected Frequency

The expected frequency is how often we think an event will happen. For example, when we flip a coin, we would expect it to land on heads half the time. So if we flipped a coin $100$100 times, we would expect it to land on heads $50$50 times (because $\frac{50}{100}=\frac{1}{2}$50100=12).

## Experimental Frequency

The experimental or observed frequency is the number of times an event occurs when we run an experiment. For example, let's say we actually decided to flip a coin $100$100 times. We expected tails to come up $50$50 times but it only happened $47$47 times. We would say that the experimental frequency for getting a tail is $\frac{47}{100}$47100. Did you notice that the experimental frequency was different to the observed frequency.

## Expected vs Experimental in Action

Now it's your turn to compare expected and experimental frequencies.

#### Instructions

1. Before you start playing with the applet, write down how often you would expect the spinner to land on each colour (i.e. the expected frequency for each colour). Discuss your answers in groups.
2. Spin that spinner! The table will record the experimental frequencies. Discuss why the probabilities change after each spin.
3. After you have finished the experiment, compare the expected frequencies to the experimental frequencies. What did you notice?

#### Worked Examples

##### Question 1

What is the probability of rolling a 3 on a standard die?

##### Question 2

A coin was flipped $178$178 times with $93$93 tails recorded.

What is the exact experimental probability of flipping tails with this coin?

### Outcomes

#### S4-4

Use simple fractions and percentages to describe probabilities