(Zippo Airlines)Suppose that in flight, airplanes engines fail with probability "q", constant and independent from engine to engine. A two engine plane makes a successful flight if at least one of the two engines work. A four engine plane makes a successful flight if2 or 3 or 4 engines work.

a.Using algebra and concept of Binomial Experiment, find the probability that a 2 engine airplane makes a successful flight. Express your answer as a formula totally in terms of "q". Remember p= 1-q. Repeat the exercise for four engines plane.

b.For what value of "q" are these airplanes equally safe? For what values are the 2 engines planes safer? For what values are the 4 engines planes safer?

(You should get a 4^th degree equation that has nice factors).