# Math Help - More probability

1. ## More probability

Hi all,
I am having problems with yet another probability revision question. Any help appreciated!

A production department has 38 similar milling machines. The number of breakdowns on each machine averages 0.04 per week. Determin the probabilities of having

a) one, and
b) less than three

machines breaking down in one week

I just can't seem to get my head round some of these probability questions!

2. You must define your distribution. Are you trying to do something else first?

We have 0.04 breakdowns per week. What kind of a distribution might that suggest? It breaks down or it doesn't...Sounds sort of Bernoulli, doesn't it? p = 0.04 (Break down) and q = 0.96 (Survive)

Maybe, but...

If we notice that we have 38 machines, it may sound as if we are running the same Bernoulli experiment 38 times.
This should sound rather Binomial, with p = 0.04, n = 38, and E[x] = 38*0.04, Var(x) = 38*0.04*0.96.

Maybe, but...

What do you think about Poisson with $\lambda = 38*0.04 = 1.52$?

Well, maybe again, but we've only 38 machines. I suppose they could break down more than once, each, but I think I'm stretching it,

Once you've pinned down the distribution, the rest can be cake. What say you?