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## Statistics and probability

### Course: Statistics and probability > Unit 7

Lesson 4: Experimental probability# Making predictions with probability

Predict the number of times a spinner will land on an elephant.

## 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?(34 votes)
- Yes, I believe that you are correct.(5 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!(19 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%(11 votes)- depends on how many questions there are and how many answers it asks for(4 votes)

- *What grade is this appropriate for?*(5 votes)
- any grade. a super smart kindergartner, a
*coolege*student, really anybody can learn this.(12 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.(4 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.(5 votes)

- Does Sal write with a apple pen or a mouse?? 'Cause trying to write with a mouse is
**VERY**hard.(3 votes)- i think a pen, and yes, i agree with you there, i use a touchpad but it's still SO HARD(4 votes)

- So should it be really common or really rare to get
**exactly**120 elephants?(3 votes)- It can be kind of rare, since you can get more or less than 120 elephants (up to 210 or as low as 0 is still possible)(3 votes)

- monke doing some kind of acrobatics(4 votes)
- I assume the possibility of getting no elephant in 210 spins is the extremely low (3/7)^210, right?(4 votes)
- cant you just put the 2 where the 1 is to make 120(3 votes)
- Pretty sure that is not how that works.(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.