A power network involves three substations, A, B, and C. Overloads at any of the

Question

A power network involves three substations, A, B, and C. Overloads at any of these substations might result in a blackout of the entire network. Past history shows that if a substation A alone experiences an overload, then there is a 1% chance of a network blackout. For stations B and C alone these percentages are 2% and 3%, respectively. Overloads at two or more substations simultaneously result in a blackout 5% of the time. During a heat wave there is a 60% chance that substation A alone will experience an overload. For stations B and C these percentages are 20% and 15%, respectively. There is a 5% chance of an overload at two or more substations. During a particular heat wave a blackout due to an overload occurred. Find the probability that the overload occurred at: a) substation A alone; b) substation B alone; c) substation C alone; d) two or more substations simultaneously

Explanation / Answer

Given: P(A) = 0.6; P(B) =0.2; P(C) =0.15; P( BO|A) =0.01; P(BO|B)=0.02; P(BO|C)=0.03

P(two ormore ) =0.05 P(BO|two or more) =0.05

BO means event of blcakout

P(BO) = (0.6*0.01)+(0.2*0.02)+(0.15*0.03)+ (0.05*0.05)=0.017

During a particular heat wave a blackout due to an overload occurred. Find the probability that the overload occurred at: a) substation A alone = (0.6*0.01)/P(BO) = 0.006/0.017= 0.3529

b) substation B alone = (0.2*0.02)/P(BO) = 0.2353

similarly

c) substation C alone = 0.0045/0.017 = 0.2647

d) two or more substations simultaneously = 0.0025/0.017 = 0.1471

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