Suppose an airline with a fleet of four-engine aircraft observed that on average, an engine with normal preventive maintenance failed two times in 10,000 operating hours. Using the Poisson model, What is the probability that two or more engines on an aircraft will fail during a flying period of ten hours?
My approach (I knew it was wrong):
The new mean was 0.002 instead of 2. But I was thrown off by the number of engines. Because the Poisson formula does not have the number of trials included.
Thank you so much in advance!
Suggestions:
I would think it would be reasonable to assume that any given engine would have a $10$-hour failure probability of $\frac{10}{5000}=.002$.
If permitted, I would assume engine failures are independent.
Then I would let $X$ be the number (out of $4$) engines that failed in ten hours. So $X$ would have a binomial distribution with $n=4$ and $p=.002$. I would then determine the probability that $X\ge 2$.