Skip to 0 minutes and 3 secondsIn this video we're going to show you the spinners and how they are used with a paperclip. Basically it is a piece of paper and a paperclip. With these spinners we can get any probabilities we want, we're not limited by what you can do with coins, dice and cards, there's no noise, they're very simple to print, they're simple to use, students get the hang of them very quickly and we supply a spreadsheet with all the different spinners used in this course and in the book and also several generic spinners. You'll find that on the website and indeed it is very simple to make your own because they're just pie charts in Excel.
Skip to 0 minutes and 36 secondsLet's just see what happens when we use one. Okay, so let's see how these spinners work. You can see I have here on my piece of paper two spinners, a grey and black one and a blue and yellow one, this is just to show you we can use greyscale we don't have to use colour. They're both used in an experiment which is about the weather - is it going to be sunny? Is it going to be rainy? Blue for rain, yellow for sun - pretty self-explanatory, but with the grey-scale the labels just to make it clear. You might also notice that we've got unknown probabilities here.
Skip to 1 minute and 10 secondsIt is the case in real life we mostly don't know the probability of an event. We have to estimate it from previous experience or from data. In a moment I'll show you different spinners where we do know the probabilities. But how do we use them? Well you just need an ordinary paperclip, I've got quite a long one but small ones are fine. You just take the end, pull it out make it reasonably straight, doesn't matter if it is perfectly straight it's just going to act as a pointer. Then take a pen, or a pencil, something with a point and just pin it down in the centre of the spinner.
Skip to 1 minute and 49 secondsPut the end somewhere convenient and give it a good flick. Whoops! That wasn't very good - let's have another go.
Skip to 1 minute and 56 secondsThere it goes and it has come up on rainy. Let's demonstrate that again, using the other spinner this time. Pin it down in the centre, give it a good flick. I've held the paper with my hand this time, which is probably a good idea and it's landed up on blue, rainy. And you can just repeat that as many times as you want, to get as many items of data as you want. Here we have two spinners where the probabilities are obvious. On the left-hand one it's two thirds yellow to one third green and the right-hand one is the reverse. We can play a very simple game with this for two players.
Skip to 2 minutes and 31 secondsBasically, spin first the left-hand one, then the right-hand one, if they're the same colour player A wins and if they're different, player B wins. Let's just give it a go.
Skip to 2 minutes and 44 secondsSo I get my paperclip, pin it down right in the centre.
Skip to 2 minutes and 50 secondsAnd that's green. Do it again with the other one.
Skip to 2 minutes and 58 secondsAlso green. So that would be player A to win. You might think that because these spinners are reverses of each other that it would be a fair game and that both players would have the same chance of winning. Well it's worth having a go to see, because you may be suprised by the results.
Making a spinner
We will be making considerable use of spinners. Watch the video to see what a basic spinner looks like, and how to make one using a paperclip and the supplied template.
- Do you think that it is important that students collect their own data when learning probability?
- What advantages might spinners have over other types of apparatus (like dice)?