Question

A realistic estimate for the probability of an engine failure on a transatlantic fight is 1/14000. Use this probability and the binomial probability formula to find the probabilities of 0, 1, 2, and 3 engine failures for a three engine jet and the probabilities of 0, 1, and 2 engine failures for a two-engine jet. Carry all numbers to as many decimal places as your calculator will display. Use your results and assume that a fight will be completed if at least one engine works. find the probability of a safe fight with a three-engine jet(n=3) and find the probability of a safe fight with a two-engine jet(n=2). Write a report for the federal Aviation Administration that outlines the key issue, and include a recommendation. Support your recommendation with specific results.

Answer 1

It is given that the realistic estimate for the probability of an engine failure on a transatlantic fight is 1/14000.

Let's find the probabilities of 0, 1, 2, and 3 engine failures for a three engine jet by using binomial probability formula

Here n = 3 and p = 1/14000.

Let's use excel:

A B C 1 X 0.99978573 2 0 3 1 0.000214255 4 2 1.53050E-08 3 3.64431E-13 6

Here 1.53050E-08 = 0.00000001530050

The formulae used on the above excel sheet are as follows:

A B 1 X p BINOMDIST(A2,3,(1/14000),0) BINOMDIST(A3,3,(1/14000),0) =BINOMDIST(A4,3,(1/14000),0) BINOMDIST(A5,3,(1/14000),0) 2 0 3 1 4 2 5 3 6 7

Now, let's find the probabilities of 0, 1, and 2 engine failures for a two-engine jet.

1 X 2 0 0.999857148 0.000142847 3 1 4 2 5.10204E-09

A 1 X BINOMDIST(A2,2,(1/14000),0) BINOMDIST(A3,2,(1/14000),0) =BINOMDIST(A4,2,(1/14000),0) 2 0 3 1 4 2 5 LC

Here we assume that a fight will be completed if at least one engine works.

From the above results let's find the probability of a safe fight with a three-engine jet(n=3)

The fight will not be completed if all the three engines are failed.

The fight will be completed if at least one engine works

Therefore required probability = 1 - P( all the 3 engines are failed) = 1 - 0.000000000000364431 = 0.999999999999636

and the probability of a safe fight with a two-engine jet(n=2)

= 1 - 0.00000000510204 = 0.999999994898

The above probabilities for 2 and 3 engines are very large.

Approximately equal to 1.

So both the conditions may be preferable.