Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws?

Question

dumbcow · Answer

area = 80
1/200 = 0.2/80
so mean is 0.2 flaws per 80 sq. ft
$$P(k=0) = \frac{(0.2)^{0}e^{-.2}}{0!} = e^{-.2} = 0.8187$$

anonymous · Answer

the answer is 0.6703

dumbcow · Answer

haha oops...are we using poisson distribution here?

anonymous · Answer

yep

dumbcow · Answer

oh i had a stupid moment...can you spot my mistake?
hint: 80 goes into 200 how many times

anonymous · Answer

2.5?

dumbcow · Answer

yeah...1/2.5 = 0.4
plug in 0.4 for mean instead, then it will work out :)

anonymous · Answer

Thank you.