A power network involves in 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 stations 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 overload at two or more substations simultaneously. During a particular heatwave, a blackout due to an overload occurred. Find the probability that the overload occurred at substation A Alone; substation B alone; substation c alone; and, two or more substations simultaneously.
A power network involves in 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 stations 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 overload at two or more substations simultaneously. During a particular heatwave, a
blackout due to an overload occurred. Find the probability that the overload occurred at substation A
Alone; substation B alone; substation c alone; and, two or more substations simultaneously.
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