2. An electrical system consists of four components as shown in Figure 1 below.

Question

2. An electrical system consists of four components as shown in Figure 1 below. The systenm works if and only if components A and B work and if either of the components C or D work. The probability of each component working is shown. Assume that all components fail independently. Find the probability that this system does not works. (Be sure to define your erents and show all your work.) Provide your answer for this problem in decimal format with four digits after the decimal. 120 pts 0.9 0.9 0.9 0.9

Explanation / Answer

Answer :

0.1981

EXPLANATION:

Given:
P(A) = Probability of component A working = 0.9

P(B) = Probability of component B working = 0.9

Since A and B are in series:

Probability of the system A and B working = 0.9 X 0.9 = 0.81

Given:

P(C) = Probability of component C working = 0.9

P(D) = Probability of component D working = 0.9

Since C and D are parallel,

Probability of the system C and D working = 1 - (1 - 0.9)2 = 1 - 0.01 = 0.99

Now: The systems A & B and C &D are in series.

So, the probability of the whole system A,B,C,D working = Probability of A & B X Probability of C & D

                                                                                  = 0.81 X 0.99 = 0.8019

So, the probability that this system does not work = 1 - 0.8019 = 0.1981

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