## anonymous one year ago 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

1. horsegirl27

Well, what do you think?

2. horsegirl27

Start by finding the area of the carpet

3. horsegirl27

A=l*w length=8 width=12 A=8*12 A=?

4. anonymous

A=lxw =8x15 =120

5. anonymous

@horsegirl27

6. horsegirl27

Oops, you had 8*15, you want 8*12

7. anonymous

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

8. 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?

9. anonymous

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

10. horsegirl27

11. horsegirl27

Well, not exactly no. Next you will have to find the probability

12. anonymous

If you look at my messages above it says that I made a mistake and that the 12 should be a 15 @horsegirl27

13. horsegirl27

oh right, I'm sorry I thought you meant when you typed it in the problem.

14. anonymous

its supposed to be 8*15 so how do I solve this? @horsegirl27

15. mathmate

@Shaekitchen hint: review Poisson distribution in your notes. $$\lambda$$ equals to 2*96/100.

16. anonymous

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

17. 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).

18. mathmate

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

19. mathmate

* P(k) = ....