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:

Here 1.53050E-08 = 0.00000001530050

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

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

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.