You are here:

Advanced Math/Probability of independent events

Advertisement


Question
A tri motor plane has three engines a central engine and one on each wing. The plane will only crash if the central engine fails AND one of the wing engines also fails. The probability of failure during any given flight is 0.05 for the central engine and 0.08 for each of the wing engines. Assuming the engines operate independently, determine the probability of the plane crashing during a flight.

I just can't agree with my college teacher for the correct answer. He is for 2(0.08*0.05)+0.05*0.08^2, because the 3 engine failure is independent.
And i'm for 2(0.08*0.05)-0.05*0.08^2, because the 3 engine failure
is accounted for twice in the first multiplication.
I would be very happy if you could answer this question!

Answer
Country:   Sligo, Ireland
Category:   Advanced Math
Private:   No
Subject:   math probability
Question:   A tri motor plane has three engines a central engine and one on each wing. The plane will only crash if the central engine fails AND one of the wing engines also fails. The probability of failure during any given flight is 0.05 for the central engine and 0.08 for each of the wing engines. Assuming the engines operate independently, determine the probability of the plane crashing during a flight.

I just can't agree with my college teacher for the correct answer. He is for 2(0.08*0.05)+0.05*0.08^2, because the 3 engine failure is independent.
And i'm for 2(0.08*0.05)-0.05*0.08^2, because the 3 engine failure
is accounted for twice in the first multiplication.
I would be very happy if you could answer this question!
----------------------------------------------------
Let:

C = "central engine fails"
L = "leftwing engine fails"
R = "righwing engine fails"

p(C) = 0.05
p(L) = p(R) = 0.08  <<< those wing engines are probably made in China, right?

Then

p(crash) = p(C and [L or R])

Now, for independent events, the rules are:

P(A and B) = p(A) p(b)
p(A or B) = p(A) + p(b) - p(A and B)
         = p(A) + p(b) - p(A) p(B)


p(crash) = p(C and [L or R])

= p(C) p(L or R)

= p(C)[p(L) + p(R) - p(L) p(R)]

= 0.05 [0.08 + 0.08 - 0.08^2]

= 2(0.05)(0.08) - 0.05(0.08)^2

I think I'm with you.

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
-----------

©2016 About.com. All rights reserved.