Flaws in a carpet ten to occur randomly and independently at a rate of two every 100 square feet. What is the probability that: a) a carpet that is 8 feet by 12 feet contains three flaws

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Flaws in a carpet ten to occur randomly and independently at a rate of two every 100 square feet. What is the probability that: a) a carpet that is 8 feet by 12 feet contains three flaws

Statistics
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Well, what do you think?
Start by finding the area of the carpet
A=l*w length=8 width=12 A=8*12 A=?

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A=lxw =8x15 =120
Oops, you had 8*15, you want 8*12
Oh you know what in the question i typed 12 its supposed to be 15 sorry for the confusion. But now that I have the area then what? @horsegirl27
So, if a carpet will have 2 flaws every 100 sq ft, and the area is 96 sq ft, is there a chance there will be 3 flaws?
No I guess not because there is not enough area but if the area is 120 which is the 8*15 then it would have enough room to have 3 flaws right? @horsegirl27
I'm not sure. But since your area is 96 sq ft, your answer will be no.
Well, not exactly no. Next you will have to find the probability
If you look at my messages above it says that I made a mistake and that the 12 should be a 15 @horsegirl27
oh right, I'm sorry I thought you meant when you typed it in the problem.
its supposed to be 8*15 so how do I solve this? @horsegirl27
@Shaekitchen hint: review Poisson distribution in your notes. \(\lambda\) equals to 2*96/100.
Is that my full answer thought? Im not sure where else to take it? My prof is crap at writing notes I cant understand it.@mathmate
What I am saying is the probability is obtained by the Poisson distribution, with lambda = 0.96*2/100= expected number of flaws for 96 sq.ft, and n=3 (3 flaws).
You have to do a calculation to find P(n)=\(\large \frac{\lambda ^k}{k!}e^{-\lambda}\) \(\lambda = 2*96/100 =expected number of flaws, k=3 (flaws) ) For further information, read: http://en.wikipedia.org/wiki/Poisson_distribution
* P(k) = ....

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