Question

Question 1
An engine encounters a standard environment with a probability of 0.95, and
a severe environment with a probability of 0.05. In a standard environment the
probability of failure is 0.02, whereas in a severe environment this probability
is 0.5
a) What is the probability of failure?
b) Given that failure has occurred, what is the probability that the
environment encountered was severe?
(4 marks)

Answer 1

Answer:

X= standard environment  encountered

Y= severe environment encountered

F = failure

Step-by-step explanation:

P(X) = 0.95

P(Y) = 0.05

P(F\X)=0.02

P(F\Y)=0.5

P(F)= P(FnX) + P(FnY)

      =P(X) P(F\X) + P(Y) P(F\Y)

      =(0.95x0.02) + (0.05x0.5) = 0.044