Lesson video

Hi, I'm Mrs Dennett.

And in this lesson, we're going to be calculating experimental probabilities or relative frequencies, and use them to make predictions.

Before we begin this lesson, we need to understand the difference between theoretical probabilities and relative frequency.

Up to this point, you've probably only come across theoretical probabilities, such as the probability of getting a tail on a coin is a half because there is one tail and two outcomes, heads or tails.

This will be for a fair coin of course.

So this spinner, the theoretical probabilities of landing on each colour are listed.

There are 10 sections.

Five are red.

So the theoretical probability of landing on red as you can see is five tenths or a half.

But in reality, if you were to spin this spinner 100 times, you wouldn't really land on red exactly 50 times.

If the spinner was spun 100 times, the amount of times you landed on a red is called a relative frequency.

And the next example, we're going to look at relative frequency in more detail.

In this example, Katie is conducting an experiment, she has spun the spinner and recorded whether it landed on red using the letter R, blue using the letter B, green, G, or yellow, Y, whereas to record her results in a relative frequency table.

Relative frequency is just the number of times and events occurred in an experiment or trial, divided by the total number of trials.

So relative frequency is an estimate of probability.

Let's find the relative frequency for landing on red.

Katie lands on red 1, 2, 3, 4, 5, 6, 7, 8 times.

Let's check that again, 1, 2, 3, 4, 5, 6, 7, 8 times.

She spun the spinner 15 times, that's 15 trails.

So the relative frequency for red is eight out of fifteen.

Eight fifteenths is the fraction.

This could also be written as a decimal, but we're going to stick with fractions for this question.

We've put eight fifteenths in our relative frequency table.

And now we look at blue.

The spinner landed on blue three times.

So the relative frequency will be three fifteenths.

Again, this could be written as a decimal or simplified if you wish.

Now for green, the spinner landed on green twice, so that's two fifteenths for a relative frequency.

And finally, yellow.

This event occurred twice.

So we have two fifteenths again.

We can now use the relative frequencies to help us make estimates for if the spinner was to be spun a certain number of times.

You may already know how to calculate an estimated probability or expected frequency.

We multiply the probability by the number of trials.

So for part b, we take the relative frequency for landing on red, which is eight fifteenths, and multiply by 150, the number of trials.

So to get the expected frequency, we multiply the relative frequency by the number of trials.

Eight fifteenths times 150 gives us 80.

Remember, this is only an estimate, we expect to see the spinner landing on red 80 times if we spin it 150 times.

Here is a question for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

You can see that Mo landed on A five times.

He spun the spinner a total of 20 times.

So the relative frequency for A is five out of twenty.

We do the same to find the relative frequencies of B, C and D.

Then, we're asked to estimate the number of times the spinner will land on B if it is spun 100 times.

We take the relative frequency for B, which is seven out of twenty, or seven twentieths, and we multiply this by 100.

This gives us an answer of 35.

So if the spinner is spun 100 times, we would expect to land on B, 35 times.

Katie has continued with her experiments.

She has spun the spinner 150 times and recorded her results.

We're asked to compare her results with the theoretical probabilities and the relative frequencies for her 15 trial experiment.

In order to do this, we need to have comparable fractions or use decimals.

I've chosen to write all the fractions with a common denominator.

I have chosen 150 as my common denominator.

What do you notice? Well, the more times Katie has conducted the experiment, the closer the relative frequencies are to the theoretical probabilities.

This is true for any experiment, the more trials that you do, the more reliable the data.

In Katie's experiment, the results of the 150 trials produced probabilities that are very close to the theoretical probabilities.

This also tells us that the spinner is not biassed.

If there have been a much greater amount of one colour compared to the theoretical probabilities, then this may have indicated some bias.

So to summarise, more trials that she does, leads to more reliable results.

And this is true for any experiment.

This gives us more accurate results for the relative frequency as an estimate of the probabilities.

We can see that the spinner is not biassed in this example.

As the probabilities, the relative frequencies tend towards the theoretical probabilities.

Here is a question for you to try.

Pause the video to complete the task and restart when you are finished.

Here are the answers.

Were asked if we think that the dice is fair.

If you look at the results from Dan and Emma's experiments, we can see that two appears a lot more in both trails.

So it is possible that the dice is biassed towards the number two.

In part b, Emma says that her data is more reliable.

She is correct.

Emma has completed more trials and therefore should have more reliable data.

That's all for this lesson.

Remember to take the exit quiz before you leave.

Thank you for watching.