There are two two airplanes. One has 2 engines and one has 4 engines. Both plane

Question

There are two two airplanes. One has 2 engines and one has 4 engines. Both planes require at least 1/2 of its engines to complete a flight. The engines work properly "p" percent of the time. What is the value of "p" such that the probability of a successful flight is the same for either plane. There are two two airplanes. One has 2 engines and one has 4 engines. Both planes require at least 1/2 of its engines to complete a flight. The engines work properly "p" percent of the time. What is the value of "p" such that the probability of a successful flight is the same for either plane. There are two two airplanes. One has 2 engines and one has 4 engines. Both planes require at least 1/2 of its engines to complete a flight. The engines work properly "p" percent of the time. What is the value of "p" such that the probability of a successful flight is the same for either plane.

Explanation / Answer

Plane I has 2 engines and prob of working successfully

P(X>=1)=1-P(X=0) = 1-(1-p)2

Similarly prob for II plane to work successfully

P(Y>=1) = 1-(1-p)4

If both are to be equal then

1-(1-p)2 =1-(1-p)4

Or (1-p)2 =(1-p)4

This is possible if either p =1 or p =0

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