Question

Problem 5. (11 points) The following circuit operates if and only if there is a path of functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. What is the probability that the circuit does not operate? 0.02 0.01 0.01 0.01 0.01 0.02

Answer 1

The solution given in the pictures initially consists of 2 examples on how to find the probability of circuit operation in parallel and serial circuits.

And then it consists of the complete process of solving the given question.
*For Erampler a series circuit, (Gerenin both devices fail independently This necunt will operate only when both the devices work. Then is A and B denote events for 1st and and device. Then the probabiung for circuit operation P (ANB) a P (A) * PLB) = 0.18 0.4 (cndependent) 20.04 *For a parallel chaut, (Geren both devices haul unclependently) TW A works e t tror chec uit will operate when, a) only A works 6 only B words. c) both A and B work 60, the probability for cleaut operatien a P (AUB) 2 1 P(ANB) à - (PA) & P(B) 2 1-10.9* 0.67 1 [0.54] = 0.46

SUM csere. HU Similarly for the given quartient 0.01 DL 10.020 Ті. «я і шви моя шум - a) Only A woocks 6 onlly B woves (both B, and B. work) e) enly Cworks (betts and C work) d) only Dworks e) both A and B work enly 1 bolt B and C wouk only 9 both A and c woolk only in both c and I wort only is both A and wort only f) 30th B and work only! A, B and conly work 1) A, B and I ally work m B, C, and only work n Age and only work

so, the pewborility for circuir operation a PLAUB UCUDT zP [AU (B, 1B2) u cance) u.D] Toolba, 10-01 J . So, let my and Ma be a sections of the count My will work, operate 6, the probaricity for Mi to work is P 6) = P (BMB) = ? (B) * P (B2) -0.01 *0.0i a 0.oool unilarly for M2 (probabluty for me to work & P. (c) 2 P (cincan & (C) & (C) - 20.01$0.01 = 0.0001. 001 Now the ment turns into

0.0ool 0.02 6410.000) (0) H50.000|482 ot 10.02 Now, the probarang per Py to work is P (AUB) 2 P (A) + PCB) - PLANB) o PCA) + P(6) - P CAD A PUB) 0.27 0.0001 -(0.23 0-0001) 20.2001- 0-00002 20.20008 I the simplegled orcuit is ch0.0001111 40.02 Py Now, the probability for sy to work 5 & Ccuola (l) & PC - Pleno) 0.0001 +0.02- 0.00* 0.0001 20.020098. The further sumplished druer

150.20008 20.0200987 Now, the probability for the chuur to work klass P ( P20 P4) z P. (P3) + P(P4)- P(B31P4) 20.20008 + 0.020098 108*0.020098 = 0.216156792 The suos ability for the concuit don't operate a (-0.21.6156792) 20.7838 43208 Z 0.78