Statistic Poisson distribution question.

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Tormund
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#1
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Each of ten test tubes containing nutrient material is inoculated with 1cc of liquid containing an average of 3 bacteria per CC. Under reasonable assumptions, which should be stated calculate the probability that exactly 7 of the 10 contain at least one bacterium.

How do I set this up? I’ve found the probability of them containing more than or equal to one which was:
X~Po(3)
P(X>=1) = 1 - P( X=<0)
= 1 - 0.04979
= 0.9502
Do I finish this off by doing

10C7 * (0.9502)^7 * (1-0.9502)^3
Or is this wrong? I definitely feel like there’s something missing or I’m doing something completely wrong, thanks.
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RDKGames
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#2
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(Original post by Tormund)
Each of ten test tubes containing nutrient material is inoculated with 1cc of liquid containing an average of 3 bacteria per CC. Under reasonable assumptions, which should be stated calculate the probability that exactly 7 of the 10 contain at least one bacterium.

How do I set this up? I’ve found the probability of them containing more jab or equal to one which was:
X~Po(3)
P(X>=1) = 1 - P( X=<0)
= 1 - 0.04979
= 0.9502
Do I finish this off by doing

10C7 * (0.9502)^7 * (1-0.9502)^3
Or is this wrong? I definitely feel like there’s something missing or I’m doing something completely wrong, thanks.
Seems OK to me.
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MindTheGaps
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#3
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(Original post by Tormund)
Each of ten test tubes containing nutrient material is inoculated with 1cc of liquid containing an average of 3 bacteria per CC. Under reasonable assumptions, which should be stated calculate the probability that exactly 7 of the 10 contain at least one bacterium.

How do I set this up? I’ve found the probability of them containing more jab or equal to one which was:
X~Po(3)
P(X>=1) = 1 - P( X=<0)
= 1 - 0.04979
= 0.9502
Do I finish this off by doing

10C7 * (0.9502)^7 * (1-0.9502)^3
Or is this wrong? I definitely feel like there’s something missing or I’m doing something completely wrong, thanks.
Looks fine to me. Be sure to state your assumptions explicitly.
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Tormund
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(Original post by Rinsed)
Looks fine to me. Be sure to state your assumptions explicitly.
I’m not sure what to put as an assumption really, can you give me a little insight? Thanks for your help
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Tormund
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#5
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(Original post by RDKGames)
Seems OK to me.
I’m a bit unsure what to put as the assumption though. :/
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MindTheGaps
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(Original post by Tormund)
I’m not sure what to put as an assumption really, can you give me a little insight? Thanks for your help
You've been given an average, what assumption allows you to model it as a Poisson distribution? What assumption allows you to do the second part of the calculation?

Think about things like independence.
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Sir Cumference
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(Original post by Tormund)
Each of ten test tubes containing nutrient material is inoculated with 1cc of liquid containing an average of 3 bacteria per CC. Under reasonable assumptions, which should be stated calculate the probability that exactly 7 of the 10 contain at least one bacterium.

How do I set this up? I’ve found the probability of them containing more than or equal to one which was:
X~Po(3)
P(X>=1) = 1 - P( X=<0)
= 1 - 0.04979
= 0.9502
Do I finish this off by doing

10C7 * (0.9502)^7 * (1-0.9502)^3
Or is this wrong? I definitely feel like there’s something missing or I’m doing something completely wrong, thanks.
Adding to what others have said, you should really define what X is and also define a second random variable and state what the distribution is for this RV. Also explain what the assumptions must be to model these random variables using Poisson and Binomial distributions respectively. Your notes/textbook should give you the conditions required for this.
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