# Math Help - plane

1. ## plane

A four-engine plane flies safely if at least 2 of its engines are working. A two-engine plane works if at least one of its engines is working. The probability of failure of an engine is $q$. Find the probability that the planes fly safely.

So is it: $P(\text{four engine flies safely}) = \binom{4}{2}p^{2}q^{2} + \binom{4}{3}p^{3}q + p^{4}$ and $P(\text{two engine flies safely}) = \binom{2}{1}pq + p^2$

2. Originally Posted by heathrowjohnny
A four-engine plane flies safely if at least 2 of its engines are working. A two-engine plane works if at least one of its engines is working. The probability of failure of an engine is $q$. Find the probability that the planes fly safely.

So is it: $P(\text{four engine flies safely}) = \binom{4}{2}p^{2}q^{2} + \binom{4}{3}p^{3}q + p^{4}$ and $P(\text{two engine flies safely}) = \binom{2}{1}pq + p^2$

Yes

RonL

3. Thanks a lot. This was one where I made an educated guess (I wanted to see if I could use a Poisson for this one). But then I realized, the poission is an estimation of the binomial. So just use binomial.