SOLUTION: i) Suppose that airplane engines operate independently and fail with probability 0.35. Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find wh

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Question 897775: i) Suppose that airplane engines operate independently and fail with probability 0.35. Assuming that a plane makes a safe flight if at least half the numbers of engine run. Find whether a 6 engine plane or a 4 engine plane has a higher probability of successful flight.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
logically it would appear that the plane with 6 engines will have a probability of success greater than a plane with 4 engines.

let's see if that's true.
this appears to be a binomial probability where:

p(x) = C(n,x) * p^x * q^(n-x)

p is the probability of success which is equal to .65
q is the probability of failure which is equal to .35

for the 4 engine plane, we want the probability that 2 or more engines are operating successfully.

this would be equal to p(2) + p(3) + p(4)

for the 6 engine plane, we want the probability that 3 or more enginers are operating successfully.

this would be equal to p(3) + p(4) + p(5) + p(6).

the complete probabilities are shown n the following tables calculated by using excel.