# Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 2 • Question 5

(a) Millie is going to spin a spinner with 5 sections numbered from 1 to 5. She says that if she spins the spinner 5 times, she’s guaranteed to spin at least one 5. Comment on Millie’s statement. (b) Anna spins the spinner 50 times and records the results in the table. Calculate the relative frequency of spinning a number less than 4.

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### Video Transcript

Part a) Millie is going to spin a spinner with five sections numbered from one to five. She says that if she spins the spinner five times, she’s guaranteed to spin at least one five. Comment on Millie’s statement. Part b) Anna spins the spinner 50 times and records the results in the table. Calculate the relative frequency of spinning a number less than four.

Well, the keyword in section a is this word “guaranteed” because Millie says that if she spins the spinner five times, she’s guaranteed to spin at least one five. Well, the first thing we can say is that this is not guaranteed. So that’s our first comment on Millie’s statement.

We can also go into why it’s not. Well, what we could say as well is that the probability of spinning a five is a fifth. And that’s because the spinner has five sections numbered from one to five. So it’s gonna be one out of five or one-fifth the probability of spinning a five.

And therefore, the expected number of five spun in five spins would be one, because we said it’s one out of five. So therefore, if we spun it five times, we’d expect we get one five spun. But the key thing here is that this is not certain. This is just a probability. Any number of fives could be spun. So it could spin five fives or it could spin zero fives, because any number of fives could be spun when we spin the spinner five times.

So we’ve answered part a and we commented on Milly’s statement. Now let’s move on to part b.

In part b, Anna spins the spinner 50 times and records the results in the table. What we need to do is calculate the relative frequency of spinning a number less than four.

First of all, we need to see which numbers we’re interested in. Well, we want to calculate the relative frequency of spinning a number less than four. So therefore, we’re interested in all the spins that are less than four. So therefore, we’re interested in the frequencies associated with spinning the numbers one, two, and three.

So therefore, to calculate the total number of spins that are less than four, what we can do is add together eight, seven, and 10. And that’s because we had eight ones, seven twos, and 10 threes. And when we do that, we get a total of 25 spins that are less than four.

Well, now what we do we need to do this. Well, what we’re trying to do is calculate the relative frequency. So this is the probability according to the results that we’ve got. Well, what this is is the probability or relative frequency that we would expect for spinning a number less than four based on the data that Anna collected. And we can see that Anna spun the spinner 50 times.

So therefore, we can say that the probability of spinning less than four, which is what this notation means that I’ve written here, is gonna be equal to 25, because that was the number of spins that are less than four, over or divided by 50. That’s cause that’s the total number of spins.

Well, you could leave your answer in this form. However, as it’s nice and easy to simplify, cause we can see that both the numerator and denominator divide by 25, we can write the answer as a half. So therefore, we can say, based upon Anna’s results, the relative frequency of spinning a number less than four is a half.