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 $\displaystyle q $. Find the probability that the planes fly safely.

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