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Christian LawsonPerfect 2 years, 3 months ago
Gave some feedback: Ready to use
Elliott Fletcher 2 years, 4 months ago
Published this.Elliott Fletcher 2 years, 4 months ago
Gave some feedback: Needs to be tested
Chris Graham 2 years, 4 months ago
Gave some feedback: Has some problems
Chris Graham 2 years, 4 months ago
I'm not keen on d). It depends on your definition of getting closer  it is staying at the same value whilst the experimental is moving towards it. That's closer in my book. I think I would lose this part altogether, as I'm not sure it adds any value.
In b), I don't think that you need the bullet points under "In this case you have..." if you are later summarising the outcomes in table 2.
You advice in c) ends up being very confusing. The distribution of outcomes in the table are way off the expected, given the probabilities in table 3. I was told that the experimental probability of rolling a 3 is 0.09 and is very close to the theoretical, but it is not, it's way off.
RE your question below, yes, displaying the simplified fraction would be better.
Elliott Fletcher 2 years, 4 months ago
I think part d) will need checking, i'm not 100% sure that it's correct.
Elliott Fletcher 2 years, 4 months ago
Gave some feedback: Needs to be tested
Elliott Fletcher 2 years, 4 months ago
Thank you for the feedback Christian, i agree that it isn't really important that fractions are simplified, but do you think i should give the answer in the advice as a simplified fraction or do you think it doesn't really matter?
And i agree that it doesn't matter if the dice are thrown one after the other or at the same time so i will reword the statement accordingly.
Christian LawsonPerfect 2 years, 4 months ago
Gave some feedback: Has some problems
Christian LawsonPerfect 2 years, 4 months ago
Saved a checkpoint:
The explanatory text that was in the statement should be at the top of the advice  I've moved it.
The description of the experiment in the prompt for part a should be in the statement  it applies to every part.
I've changed "find the experimental probability of rolling a {number}" to "find the experimental probability of rolling a total of {number}".
I put the total number of trials in the statement  it's rare you'd do an experiment and not know how many times you did it, and adding up 11 numbers is a chore.
Lots of sentences in the advice start "therefore, ..."  try leaving it out, and if the sentence still makes sense leave it that way.
Is it important that the fractions are simplified? Do you need to explain how to do that in this question? I've taken away the "must be reduced" restriction, and I think the explanation of how to reduce a fraction in the advice can go.
"When two unbiased 6sided dice are rolled together, the total shown on the faces has to be between 2 and 12. There are 36 possible outcomes when adding the faces of two dice together" is incorrect. There are 11 outcomes after adding. There are 36 outcomes when rolling two dice, one after the other. When two indistinguishable dice are thrown at the same time, you could make a case that there are 18 outcomes. This will trip students up, so it's important to be very clear.
Can you convince yourself that it doesn't matter if the dice are thrown one after the other or at the same time, if you're only looking at the total score? Can you rephrase the statement about the number of outcomes so that it's obvious?
I haven't got time to look at the last piece of advice, but it looks like there isn't any for part d. The table for part c should make it clear that this is just one sample, not the results you'd get every time.
Elliott Fletcher 2 years, 4 months ago
Gave some feedback: Needs to be tested
Chris Graham 2 years, 4 months ago
As discussed, would be better as two questions with separate parts. In part (b) the student will answer the second two gaps based on their interpretation of the coin's bias, and offering feedback after the first bit would then set them down the right track.
The drop down question should work with the opposing terms either way round. This would require a marking matrix (it would need to be its own part, but I've suggested you do that anyway), or this could be replaced with multiple choice statements.
I don't think "Is this coin biased?" is a fair question here: statistically it may or may not be, so as suggested you could replace this with two experiments, with a distractor set of results for small N, and then ask the student which coin is more likely to be biased. This is assessing their understanding that the experimental approaches the theoretical probability.
Elliott Fletcher 2 years, 4 months ago
Created this.Name  Status  Author  Last Modified  

Theoretical Probability vs Experimental Probability  Ready to use  Elliott Fletcher  01/08/2017 13:25  
Hugh's copy of Theoretical Probability vs Experimental Probability  draft  Hugh O'Donnell  16/01/2018 13:46  
Theoretical Probability vs Experimental Probability  draft  Xiaodan Leng  11/07/2019 01:59 
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This question is used in the following exams:
 Probability by Elliott Fletcher in Elliott's workspace.
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