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Current time:0:00Total duration:5:05

Making predictions with probability

Video transcript

so right over here I have the type of spinner that you might see in a child's game you can see there's seven equally likely possibilities let's see there's one two three four five six seven equally likely possibilities it looks like in four of them you have you use fun and elephant two of them you have this Mouse running away from something and then in one of them you have this this monkey doing some type of acrobatics fair enough now let's let's pose ourselves an interesting question at least I think it's an interesting question let's say we were to spin the spinner 210 times so we're going to spin 210 we're going to spin that spinner 210 times and I want you to make a prediction I want you to predict I want you to predict the number of times number of times we get an elephant we get an elephant number of times we get an elephant out of the 210 times so why don't you have a go at it all right so you've assumed 'video and had a try so one one way to think about is well for one spin what is the probability of getting an elephant so let's do this one spin so for one spin what is the probability of getting an elephant well let's see there are we have already talked about this is a fair spinner there are seven equally likely possibilities and then how many involve getting an elephant well so we have one two three four four out of the seven equally likely possibilities involve us getting an elephant so one reasonable thing to do and this is actually what I would do is it's going to look for a four sevens probability means I should expect that 4/7 of the time over especially if I'm doing a lot of these expecting it over and over and over again it's a reasonable expectation that a 4/7 of the time I we'll get an elephant I've just calculated the theoretical probability here based on this being a fair spinner and that should inform that if I were to do a bunch of experiments that 4/7 of the time that that I should see the me getting the elephant so it would be reasonable or reasonable prediction to say look I'm going to I'm going to spin this thing 210 times and I would expect that 4/7 of those 210 times I would get an elephant and so let's think about what this is 210 times 4/7 210 divided by 7 is 30 30 times 40 is 120 so 120 times my prediction or maybe your prediction was this as well all right so I think it's a reasonable prediction is that if I spin it 100 if I spin it 210 times then I'm going to get an elephant 120 times that's very important to think about what this is saying and this is not saying is it possible that I get an elephant under 21 times or maybe 119 times sure sure it's completely reasonable that you might get something different than this in fact there's some probability that you get no elephant that you know if you consider getting an elephant lucky that you just you just happen to keep landing on the monkey or one of the mice now it's a very low probability that that would happen if you've got it two hundred ten times but it is it is possible so it's important to realize that this is just a pretty there's actually a possibility that you might get an elephant on all 210 spins once again that's a low probability but it is possible so this isn't saying that this is you're definitely going to get it 110 you're definitely going to get the elephant 120 times in fact it's very reasonable that you might get the elephant 123 times 128 times or 110 times or even 90 times these are all completely reasonable things to to happen all you would say is that look if I had to predict it this out of all of the different you know I can I can get an I can get the elephant anywhere between 0 and 200 and ten times out of all of those possibilities before I even start spinning I'll say okay you know I think that this is the this is the most reason one that I'm going to get 4/7 of the time but it's not saying that hey yeah this is it's not saying that I'm I'm definitely going to get it 120 times it's not saying that 118 times or 129 times aren't reasonably possible as well it's just saying look this is a reasonable prediction I'm using the experimental probability it's four sevens probability and so if I'm going to do something 210 times well I could expect that it's going to happen 4/7 of the time I don't know if we're sure that it's going to happen 4/7 of the time but that is a reasonable prediction to make