Approximations and hypothesis tests question ( need help )

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MrNobody579
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Three unbiased tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown 160 times. Using a suitable approximation, estimate the probability of getting at least two ‘treble fours’.

I'd extremely appreciate it if someone can send a worked solution for this! Thanks
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Luwei
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(Original post by MrNobody579)
Three unbiased tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown 160 times. Using a suitable approximation, estimate the probability of getting at least two ‘treble fours’.

I'd extremely appreciate it if someone can send a worked solution for this! Thanks
Are you in university? I mean the thing is the tetrahedron does not have equally-sized faces so the probabilities are not as simple as 1/4?
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tej3141
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(Original post by Luwei)
Are you in university? I mean the thing is the tetrahedron does not have equally-sized faces so the probabilities are not as simple as 1/4?
They said unbiased in the question so I think you can assume the probability of each is 1/4. Theres no need to over complicate it
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MrNobody579
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(Original post by Luwei)
Are you in university? I mean the thing is the tetrahedron does not have equally-sized faces so the probabilities are not as simple as 1/4?
Unbiased, so it is 1/4 for each.
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tej3141
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(Original post by MrNobody579)
Unbiased, so it is 1/4 for each.
Well I believe you would find the probability for a treble four (1/4)^3. Then use this in a binomial distribution with n =160 and p = the probability of a treble 4. Then calculate p(x>=2)
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username1732133
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(Original post by MrNobody579)
Three unbiased tetrahedral dice, each with faces labelled 1, 2, 3 and 4, are thrown 160 times. Using a suitable approximation, estimate the probability of getting at least two ‘treble fours’.

I'd extremely appreciate it if someone can send a worked solution for this! Thanks
The Poisson distribution is suitable in this case. A normal approximation will not be very accurate. These questions seem a bit pointless now that your calculator will not have a problem with the binomial distribution for this question.

You can compare results here: https://burymathstutor.co.uk/compareapprox.html
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