Question

An engine encounters a standard environment with a probability of 0.9, and a severe environment with a probability of 0.1. In a normal environment the probability of failure is 0.03, whereas in the severe environment this probability is 0.5.

i. What is the probability of failure?
ii. Given that failure has occurred, what is the probability that the environment encountered was severe?

Answer 1

.077

.64935

Explanation:

Let F= failure

let S= severe

we are given that

p(F|S')= .03

p(F|S)= .5

For the first question we are looking for f

we can solve for it by using the law of total probability

so in theory we want

F∩S+F∩S'

Using the conditional probability formula we can solve for the intersections

.03*.9+.5*.1= .077

2.

For this question we are looking for S|F

to solve this use bayes thereom

`S|F=(F|S*S)/(F|S*S+F|N*N)=(.5*.1)/(.5*.1+.9*.03)=.649` (or 50/77)