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### Course: Get ready for AP® Statistics>Unit 5

Lesson 1: Predictions with probability

# Making predictions with probability

Predict the number of times a spinner will land on an elephant. The theoretical probability helps us get close with our prediction, but we can't know for sure until we actually spin the spinner.

## Want to join the conversation?

• I think that probability is more about the chance of what will happen in future events and you try and predict that. Am I right?
(44 votes)
• Yes, I believe that you are correct.
(11 votes)
• What if the following information is given?
1. Where is the arrow pointing at the starting of the experiment?
2. Approximately how many times does it go through the entire circumference in each roll?
--> Will that affect the probability?
(17 votes)
• Yes, where the spinner starts and how many times it goes around the spinner are both factors, but the amount of force you put on it is one of the most important factors that is extremely hard to be intentionally duplicated, so it is very hard to force the spinner to land on a certain triangle.

Here it is all laid out.

Probability = Factor( Starting point, Force, Weight of arrow, ......)
Force = How hard you push or flick or hit the arrow
Force = MPH (Miles per hour) If you flick the arrow extremely hard, it will go faster.
If you start on the monkey and flick it so that it spins three times completely around, and ends up on the elephant next to it, then if you applied the same amount of force to the arrow starting on the mouse next to the monkey, then you know it will land on the monkey.
The problem is, it is very hard to apply the exact amount of force to make the arrow land on a certain triangle over and over.

I hope this helps! Have a great day!
(22 votes)
• If you had to choose an answer to this question at random, what is the chance you will be correct?

A)25%
B)50%
C)0%
D)25%
(13 votes)
• depends on how many questions there are and how many answers it asks for
(8 votes)
• *What grade is this appropriate for?*
(6 votes)
• any grade. a super smart kindergartner, a coolege student, really anybody can learn this.
(14 votes)
• How do you figure the possibility of getting the elephant all 210 times?
(6 votes)
• That's a nice question! For independent events (in this case, every spin is independent, meaning it's not related to the previous spins), the probability of a specific outcome happening across all these events is found by multiplying the probability of the event happening once by itself for the number of events. In other words, you raise the probability of the event happening to the power of the number of events.

To answer your question, in our example the probability of spawning an elephant is 4/7 and the number of spins is 210, then the probability of getting an elephant on all 210 spins is (4/7)^210.

This number is astronomically small and, it's virtually zero. So for all practical purposes you could say it's impossible to spawn 210 elephants in 210 spins.
(9 votes)
• Does Sal write with a apple pen or a mouse?? 'Cause trying to write with a mouse is VERY hard.
(5 votes)
• i think a pen, and yes, i agree with you there, i use a touchpad but it's still SO HARD
(3 votes)
• I am having difficulty with this problem:
Three coins are tossed simultaneously 250 times. The distribution of various outcomes is listed below :
(i) Three tails : 30,
(ii) Two tails : 70,
(iii) One tail : 90,
(iv) No tail : 60.
Find the respective probability of each event and check that the sum of all probabilities is 1.
(3 votes)
• They are asking this: you are told that three coins are being flipped at the same time; what is the probability of each event? The values they give you are actually not necessary, since you know that any coin toss is 50/50.

So toss three coins: they each have a 50% chance of being tails. You can make a tree where the branches split into the possibilities, and then count how many there are. Then the chance for each outcome is how many times it actually happens, divided by the total number of outcomes. All the possible outcomes added together should give you 1, which is also 100%. Try it, and tell me how it goes!

Ps, there are certainly videos on KA about questions like these. If you continue to have trouble, I will find them for you.
(6 votes)
• I assume the possibility of getting no elephant in 210 spins is the extremely low (3/7)^210, right?
(5 votes)
• When you flip a coin, isn't the possibility of getting all heads the same as getting heads, tails, heads, tails, heads, tails, and so on the same? So, I am saying that isn't getting exactly a one-in-two chance of getting heads the same probability of getting all heads?
(3 votes)
• Your first statement is correct. But for your second claim, I'm not sure what do you mean. Do you mean that getting 1 head has the same probability of getting all heads in a certain amount of flips?
(4 votes)
• what happens if it lands on the line<? Could you find out how many times that might happen??
(3 votes)
• if the spinner lands on the line dividing two sections, it's usually considered as landing on both sections simultaneously or neither section, depending on the specific rules of the game. without additional information about how the spinner behaves when landing on the line, it's difficult to determine the outcome
(3 votes)

## Video transcript

- [Voiceover] So right over here, I have a 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've spun an elephant. Two of them, you have this mouse running away from something, and then in one of them, you have this monkey doing some type of acrobatics, fair enough. Now 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 to have a go at it? All right, so you've, I'm assuming, like always, pause the video and then had a try. So one way to think about it, 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, 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 go, look, a 4/7 probability means I should expect that 4/7 of the time, especially if I'm doing it over, and over, and over again, it's a reasonable expectation that, hey, 4/7 of the time, I will 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 I should see me getting the elephant. So it would be a reasonable prediction to say well, look, 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 seven is 30. 30 times 40 is 120. So 120 times. My prediction, or maybe your prediction was this as well, I think it's a reasonable prediction, is that if I spin it 210 times, that 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 121 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. If you consider getting an elephant lucky, that you just happen to keep landing on the monkey or one of the mice, and that's a very low probability that that would happen if you spun it 210 times, but it is possible. So it's important to realize that this is just a prediction. 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 you're definitely going to get the elephant 120 times. In fact, it's very reasonable, that you might get the elephant 123 times, or 128 times, or 110 times, or even 90 times. These are all completely reasonable things to happen. All you would say, is that, look, if I had to predict it, this, out of all of the different... I can get the elephant anywhere between zero and 210 times, out of all of those possibilities, before I even start spinning, I'll say, okay, I think that this is the most reasonable one, that I'm going to get it 4/7 of the time. But it's not saying that, hey, that 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, 4/7 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 for sure that it's going to happen 4/7 of the time, but that is a reasonable prediction to make.