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oasis77 · Feb 10, 2011, 01:22 AM

hello, I am doing this probability and got stuck with it.
I am not sure where to start with, so if you think there is a way, please help me
Do I need a combination here?

A four-engined aircraft can fly safely on two engines; a three-engined aircraft can fly safely on one. On a particular trip, the probability of any engine failing is p, independently of all other engines and of the aircraft type.

which type of aircraft has the highest probability of being able to make this journey safely?

Unknown008 · Feb 10, 2011, 03:30 AM

Let's take first the 4-engined aircraft.

What is the probability that it makes it's journey safely? It's the event where there are 4 good engines, 3 good engines or 2 good engines. Or the opposite of having only 1 good engine or no good engine at all.

The latter is shorter. So, find the probability that there is either only 1 good engine or no good engine.

This is a binomial distribution, and let X be the event an engine is good.

X ~ B(4, p)

$P(X = 1) = 4C1(p)^1(1-p)^3$

$P(X = 0) = 4C0(p)^0(1-p)^4$

Now, add both since in both cases, the plane cannot fly safely.

Can you try with the other plane now and post what you get? :)