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Pascals triangle
I have a question about how to use the numbers in the pascal triangle to determine certain probabilities. Lets assume I have used inclusion-exclusion principle to solve a certain question and have come up with exactly five terms. Do I have the right multiplyers for the following questions.
1. One or more term one - term two + term three - term four + term five 2. Exactly one term one-2*term two+3*term three-4*term four+5*term five 3. Two or more term two - 2*term three + 3*term four - 4*term five 4. Exactly two term two - 3*term three + 6* term four - 10*term five 5. Three or more term three - 3*term four + 6*term five 6. Exactly three term three - 4*term four + 10*term five Am I doing this correctly. Thank you, Cobra |
#2
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Re: Pascals triangle
[ QUOTE ]
I have a question about how to use the numbers in the pascal triangle to determine certain probabilities. Lets assume I have used inclusion-exclusion principle to solve a certain question and have come up with exactly five terms. Do I have the right multiplyers for the following questions. 1. One or more term one - term two + term three - term four + term five 2. Exactly one term one-2*term two+3*term three-4*term four+5*term five 3. Two or more term two - 2*term three + 3*term four - 4*term five 4. Exactly two term two - 3*term three + 6* term four - 10*term five 5. Three or more term three - 3*term four + 6*term five 6. Exactly three term three - 4*term four + 10*term five Am I doing this correctly. Thank you, Cobra [/ QUOTE ] That's correct. You use the same coefficients for "exactly n" as for "n + 1 or more", and the coefficients come from Pascal's triangle with every other term negated as you have shown. This post explains the generalized inclusion-exclusion method, and here is another example. Did you get this from me? I haven't seen this anywhere else, though I'm sure it must appear somewhere. |
#3
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Re: Pascals triangle
Yes BruceZ I did get this from you. It was about two years ago and when I searched for it I was unable to find it. You were answering some questions on inclusion-exlusion. I thought I remembered it but I just wanted to confirm it. I thought that there was a catch on the last term. Something like if you determine all terms of the probability question that the last term had a different multiplyer. Thanks for your response.
Cobra |
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