A system consists of four components connected as shown.

Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.1, 0.2, 0.05, and 0.3, respectively, what is the probability that the system functions?

Given, a system consists four component A,B,C and D.

From the given diagram

A be the event that component function is A.

B be the event that component function is B.

C be the event that component function is C and

D be the event that component function is D.

Here we assumed independently function is A,B,C and D.

Our goal is to find

a). What is the probability that the system functions?

Step 1 of 1 :

If the probability fails

A=0.1, B=0.2, C=0.05 and C=0.3.

Then,

P(A) = 1-0.1

P(A) = 0.9

P(B) = 1-0.2

P(B) = 0.8

P(C) = 1-0.05

P(C) = 0.95 and

P(D) = 1-0.3

P(D) = 0.7

Now we have to find the probability that the system functions.

From the diagram 3 subsystem is there.

Therefore

We have to...