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Old 05-04-2019, 10:44 AM
actuaryxjh actuaryxjh is offline
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Default One problem in SOA study manual

Hi everybody, I am confused by this problem:

I think, in terms of calculating the probability, we should not use combination, rather, we should use permutation, because the order actually matters (picking QND counts differently from picking DNQ), so my solution would be

total: 6*5*4 = 120

one Q: 4*3 = 12

two Q: 4

probability would be (12*2+4)/120

what is wrong with my thoughts? thanks~
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Old 05-04-2019, 11:09 AM
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Gandalf Gandalf is offline
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You need to explain yourself. Why does order matter, and where did your calculations except 6*5*4 come from?

You could use permutations, with 120 as the denominator, as long as you use the correct corresponding numerator. There is no need or advantage to using permutations.
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Old 05-04-2019, 11:32 AM
actuaryxjh actuaryxjh is offline
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Quote:
Originally Posted by Gandalf View Post
You need to explain yourself. Why does order matter, and where did your calculations except 6*5*4 come from?

You could use permutations, with 120 as the denominator, as long as you use the correct corresponding numerator. There is no need or advantage to using permutations.
I don't know how to express my thoughts, but I feel like combination is not correct, order really matters in this case.
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Old 05-04-2019, 11:42 AM
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If you want to use order, write down all the possible orders that work, and then calculate how many ways there are of getting that order. You would then conclude that the combination method works.

For example, Qnd works, and there are 2*3*1 ways of getting that order.
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Old 05-04-2019, 11:56 AM
Academic Actuary Academic Actuary is offline
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For this particular problem the easiest way is to calculate the probability of the complement which is the probability of not picking a quarter. You could do this by multiplying probabilities (4/6)(3/5)(2/4) or by using a counting rule.
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Old 05-06-2019, 03:47 PM
actuaryxjh actuaryxjh is offline
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Thank you Gandalf and Academic Actuary~
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