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 has shown that if 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 heatwave 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 simultaneously. During a particular heat wave a blackout due to an overload occurred. Find the probability that the overload occurred at substation A alone; substation B alone; substation C alone; two or more substations simultaneously.

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P blackout during a heat wave 001 60 002 20 003 15 005 5 170 Conditional probabiliti... View the full answer