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tennyson
guest

Mar1605, 04:13 PM (EST) 

"probability"

I'm an adult but stumped by the answer to this 5th grade test problem: Sam spins the spinner 18 times with the following results  Grape = 5 Apple = 4 Orange = 6 Pear = 3 Based on these results, what is the probability that Jule's spinner will land on the apple on his next spin? The answer given was 2/9. That is the % that it has landed on apple in the first 18 spins but does that truely reflect the probability that it will do so on the next spin?


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Mark Huber
guest

Mar2105, 02:27 PM (EST) 

2. "RE: probability"
In response to message #0

The question was poorly worded. A better way to state the question would be: "Based on these results, estimate the probability that Jule's spinner will land on the apple on his next spin?" The question is not really a probability question; it is a statistics question. Given some data, make an inference about properties concerning how the data were generated. To solve any problem like this, an explicit'statistical model must be constructed. The model implied by the statement of the problem is a simple one: 1) Each spin is independent of the others. 2) Each spin has the same probability of landing on apple. Given this (simple) model, then the classical statistical estimate of the probability that the spinner comes up apple is just the number of times it came up apple divided by the number of spins, as you indicated. But this is only a statistical estimate of the probability, and might not necessarily be the exact probability. This raises a great number of questions about how close such an estimate is to the true answer, many of which are dealt with in an introductory course (or text, or website) on statistics. Mark Huber 

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Calculette
guest

Jul2905, 07:14 AM (EST) 

3. "RE: probability"
In response to message #2

Just looking at the question.......doesn't the fact that it'says "based on these results" mean that it wants you to use the probability calculated by the first 18 spins....that is 4/18 for the apple....therefore the chance of getting the apple is 4/18 or 2/9. If, instead, it just asked for the probability of the next spin being an apple, (without being asked to take the previous results into account), then the answer would be 1/however many possible outcomes there were. (I forget how many now) I think the solution is directly related to those four words "based on these results". 

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Mark Huber
guest

Jul3005, 02:47 PM (EST) 

4. "RE: probability"
In response to message #3

>Just looking at the question.......doesn't the fact that it >says "based on these results" mean that it wants you to use >the probability calculated by the first 18 spins....that is >4/18 for the apple....therefore the chance of getting the >apple is 4/18 or 2/9. >If, instead, it just asked for the probability of the next >spin being an apple, (without being asked to take the >previous results into account), then the answer would be >1/however many possible outcomes there were. (I forget how >many now) >I think the solution is directly related to those four words >"based on these results". The point Calculette, is that it is impossible to know exactly what the probabilities are from the previous answer. Suppose that each of the colors was equally likely. Then there is still a positive probability that the data that appeared in the first 18 tries could have arisen purely by chance. The data doesn't allow to calculate the probabilities exactly. What you can do is use the data to estimate the probabilities, but that is different. For instance, suppose that I told you that Kanesha was 3 foot 6 inches tall, and I asked: what age is Kanesha? You could estimate her age based on what you know about the heights of children given their age, but you don't have enough information to say for sure what her age is. In the same way, given the first 18 spins, you have some information about the chances of various colors, but you do not have enough information to exactly say what they are. And that is why the question was poorly worded: it asked for the probabilities, rather than just an estimate of the probabilities. Mark Huber 

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TheSmith
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Aug2905, 03:13 PM (EST) 

6. "RE: probability"
In response to message #0

First off, I agree with everyone else on here that the problem is poorly worded. I think we all agree on that. The problem is that we're thinking about the theoretical probability, which we can't determine from the given information and the experimental probability, which we can determine from the given information. The former is based on what should happen and the latter is the product of what has happened. The two aren't always the same and in most cases, given enough randomness inherent to the problem, are unlikely to be. As an example, let's say that you flip a coin 1000 times. The center of that distribution, which is the most likely outcome, would be 500 H/500 T, but at the same time, it's very unlikely for that to happen exactly like that since there are so many other outcomes possible. They are all less likely, but there's just so darn many of them. Anyway, if the problem said "Based on these results, what is the experimental probability of Jule's spinner landing on the apple on his next spin", then the 2/9 answer makes sense. On a side note, if we're looking for the actual spinner itself, it's impossible. The spinner could be broken into four equal pieces, each 25% of the area of the spinner (taken radially, of course) and due to randomness and sampling variation, we got something like (5, 4, 6, 3). In case you are really curious, there's a test that you can run to see if this is possible called a chisquare test and when I ran it, those outcomes passed meaning that it is statistically reasonable that these results came from a spinner in four equal pieces. If we want to look at this as a strictly statistical question, it becomes much more complicated looking for the boundaries that would still produce these results a comfortable enough of the time. (In other words, if it could happen, but it would happen less than 5% of the time, it's not really reasonable to think that spinner produced those results.) The problem is obviously looking for the experimental probability, but forgot to say that, so we're all expecting to be looking for the theoretical probability. Since finding the TP is impossible, we should assume that we're looking for the EP, but some explicit directions would be nice, especially for a 5th grader. 

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Teacher
guest

Mar0106, 02:13 PM (EST) 

7. "RE: probability"
In response to message #0

There are 2 types of probability. One is experimental the other theoretical. In theory, we say that your results will be typical of your first 18 spins. If you continue to experiment, you may not get the same results as you would see "in theory". We teach the kids here that to get the best results from an experiment you have to perform it numerous times. The more times an experiment is performed, the closer your experimental results will be to the theoretical results. Hope this makes sense! 

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alexb
Charter Member
1952 posts 
Mar0306, 00:07 AM (EST) 

10. "RE: probability"
In response to message #7

>There are 2 types of probability. One is experimental the >other theoretical. I do not think that the concept of experimental probability may possibly hold water. And this for the following reason: >In theory, we say that your results >will be typical of your first 18 spins. Since the chances are slim that the next 18 spins will produce the same distribution, which is typical? >If you continue to >experiment, you may not get the same results as you would >see "in theory". Most certainly you will not, worse yet your previous experiment will not be repeated! >We teach the kids here that to get the >best results from an experiment you have to perform it >numerous times. The more times an experiment is performed, >the closer your experimental results will be to the >theoretical results.
Even this may not be true. The more times an experiment is performed the higher are the chances that the distribution will be close to the theory. There is one and only one probability, which can be estimated experimentally. The notion of experimental probability is not only confusing and unnecessary, it is impractical. 

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Wu
guest

Mar0506, 07:30 PM (EST) 

11. "RE: probability"
In response to message #10

So maybe, the teacher exposes the limitations of the information given, uses the various student responses of the classroom to discuss the fallibility of incomplete data and conditions, and has a great class. 

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Susan Zagryn
guest

Jan2107, 09:06 AM (EST) 

14. "RE: probability"
In response to message #0

If this is the problem in its entirety, then it is definitely, poorly written. However, if there was an illustration of the spinner or a Description that the spinner only had the four fruits on it, then the answer is: there is a one in four (1/4) probability that it will land on the apple on his next spin. There are four possibilities and with every spin it will land on only one fruit. 

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Kevin
guest

Jan3007, 07:44 AM (EST) 

15. "RE: probability"
In response to message #14

If we say that the probability of landing on Apple is 1/4 we are assuming 2 things. 1. The number of fruits is limited to those listed which was stated earlier and 2 the size of the area for each fruit is the same size. Given both of those assumptions the data given is really the closest that you can get to making a guess at the probabilty because we dont know any other parameters. With that being said 2/9's is the answer. 

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