Homework Help: Poisson distribution problem

1. Nov 7, 2015

skrat

1. The problem statement, all variables and given/known data
We assume that the number of structural flaws on a long wire have obey Poisson distribution law. On average we find 1 flaw every 5 meters.

a) What is the probability that a 20 m long section will have maximum 2 flaws?
b) We slice the wire into 1 m long sections. What is the probability that 3 or less sections (out of 10) have one flaw or more?

2. Relevant equations

3. The attempt at a solution

a) $$P=e^{-0.2\cdot 20}(1+0.2\cdot 20+\frac{(0.2\cdot 20)^2}{2})=0.238$$
b) Probability that there is NO mistake on a 1m long section is $$P=1-e^{-0.2}=0.18$$ now using Binomial distribution the probability should be $$P=1-\sum _{i=0}\binom{10}{i}(1-0.18)^i0.18^{10-i}$$ yet the results I have say that $$P=1-\sum _{i=0}\binom{10}{i}0.18^{i}(1-0.18)^{10-i}.$$

I personally disagree with that "official" result but would like to hear your opinion...!

2. Nov 7, 2015

skrat

Ah, forget it.

b) The probability 0.18 applies to that there is at least one (or more) flaw on a 1 m section.