Identifying valid simulations
About this video
A theater manager simulates 50 visitors, where about 40% buy popcorn, by drawing from a bag of 2 green and 3 white marbles with replacement. The simulation is accurate because the chance of drawing green (2/5 = 40%) matches the chance a visitor buys popcorn, and replacing the marble keeps that chance the same on every draw.
You'll be able to
- judge whether a simulation matches a real situation's probability.
- explain why drawing with replacement keeps the probability the same each time.
- explain why a simulation doesn't guarantee an exact number of outcomes.
Key words
- simulation
- Using a chance tool, like marbles or coins, to act out a real situation.
- replacement
- Putting an item back after drawing it so the next draw has the same chances.
- probability
- How likely something is, as a fraction, decimal or percent.
Transcript
- [Instructor] We're told that at a movie theater, about 40% of the visitors buy popcorn. The manager wants to simulate whether each of the next 50 visitors will buy popcorn. He places five marbles in a bag: two green marbles to represent a visitor buying popcorn and three white marbles to represent a visitor not buying popcorn.
He draws a marble 50 times, replacing it after each draw. Why does this simulation accurately represent the situation? So why don't you pause the video and have a go at that? Okay, so before I even look at the choices, let's just think about what's going on. So we know that 40% of the visitors buy popcorn.
I would argue that if we knew that, it, kind of, you don't need to do the simulation anymore. Usually you do a simulation so that you can get at an estimate of the probability, but let's just run with it. Let's just say we know that. And so I guess this manager just wants to see what happens if you simulate it with marbles.
Although, once again, you would normally go the other way around. You do the simulation in order to figure out the probability. But let's see, 40% chance. So if two out of the five are green marbles, every time he picks one out, there's a two out of five chance.
Two out of five is equal to four out of 10, which is the same thing as a 40% chance. So it does seem like a reasonable way of having a 40% chance, and every time, he draws the marble and he replaces it. If he didn't replace it, it would actually change the probability for the next draw.
But by replacing it every time, there's exactly a two out of five or four out of 10 or a 40% chance. So I would say it does represent the situation because this two out of five is 40%. So, let's see. Choice A, the simulation is accurate because marbles are always a better random device than coins or spinners.
No, that's not necessarily the case. Coins or spinners can be fine. Replacing the marble after each draw guarantees that exactly 20 green marbles will be drawn. Well, no, we don't even know that 20 green marbles will be drawn. You definitely can't guarantee that.
The probability of drawing a green marble is the same as the probability that a visitor buys popcorn. Yes, that's what we said. Two out of five is 40%, which is the probability that a visitor buys popcorn. The simulation is accurate because there are 50 draws for 50 visitors.
No, I wouldn't go with that either. And just to give a little bit of credit, I know I was saying, "Hey, you know, normally, you would do the simulation in order to figure out the probability." I guess part of the value here is to figure out what is the distribution of outcomes when you actually do it 50 times.
So maybe he could do it 50 times, multiple times, and then, anyway, I don't want to get into it. So there could be some value of actually doing this simulation. But either way, I like choice C.
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