#1
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need a probability formula
there are X marbles in a bowl. Y number of them are red. if i pick out Z marbles, what is the probability i will have at least 1 red marble? at least 2? what about exactly 1 or 2?
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#2
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Re: need a probability formula
For the probability you have at least 1 red marble it is best that you take the complement for when you select no red marbles .
P(r=0) = c(x-y,z)/c(x,z) p(r=1)+p(r=2)+...+P(r=y)= 1-P(r=0) = 1-c(x-y,z)/c(x,z) b)Since we know p(r=0) , we need to figure out p(r=1) . c(y,1)c(x-y,z-1)/c(x,z). So now take 1-p(r=0)-p(r=1) to get your answer . c) Just add p(r=0)+p(r=1) since these probabilities are independent . |
#3
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Re: need a probability formula
[ QUOTE ]
For the probability you have at least 1 red marble it is best that you take the complement for when you select no red marbles . P(r=0) = c(x-y,z)/c(x,z) p(r=1)+p(r=2)+...+P(r=y)= 1-P(r=0) = 1-c(x-y,z)/c(x,z) b)Since we know p(r=0) , we need to figure out p(r=1) . c(y,1)c(x-y,z-1)/c(x,z). So now take 1-p(r=0)-p(r=1) to get your answer . c) Just add p(r=0)+p(r=1) since these Events are mutually exlusive . [/ QUOTE ] FYP PairTheBoard |
#4
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Re: need a probability formula
Yup mutually exclusive, that's what I meant to say :P
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#5
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Re: need a probability formula
could you explain the meaning of this:
c(x-y,z)/c(x,z) thanks. |
#6
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Re: need a probability formula
Here is an example .
If you want to know the number of ways of selecting 3 kids from 10 , the total number of ways this can occur is c(10,3) .If you care about the order in which you select them , then it is p(10,3) . Since in your example , we don't care about the specific order in which you select marbles so we use the C notation . In general C(x,z) is the number of ways of selecting z marbles from a bowl containing x . We must specify that x>=n for this to make any sense . Since there are y red marbles in a bowl containing x marbles in total , it must be true that there are x-y non red marbles . We must select z from x-y non red marbles, this is just C(x-y,z) . The denominator , which is the total number of ways of selecting z from x marbles is c(x,z) . The next step is to divide the number of favorable cases over the total number of cases . |
#7
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Re: need a probability formula
FWIW, your computational time could be avoided in most cases if you use some binomial probability tables (assuming you know how to use them after reading the previous posts).
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