4. Suppose the probability of an engine failing during flight is $1-P$. And whether each engine fails is independent. If at least $50 \%$ of the engines are operating normally, the plane can fly successfully. If a 4-engine plane is to be safer than a 2-engine plane, the range of values for $P$ is
A. $\left(\frac{1}{3}, 1\right)$
B. $\left(0, \frac{2}{3}\right)$
C. $\left(\frac{2}{3}, 1\right)$
D. $\left(0, \frac{1}{4}\right)$
4. C The probability of a plane with 4 engines operating normally is $p^{4}+4 p^{3}(1-p)+6 p^{2}(1-p)^{2},$ and the probability of a plane with 2 engines operating normally is $p^{2}+2 p(1-p),$ solving this yields $p>\frac{2}{3}$.