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 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 heat wave there is a 64% chance that substation A will experience an overload, a 24% chance that substation B will experience an overload, and a 19% chance that substation C will experience an overload. There is a 3% chance that exactly two of the substations will simultaneously experience overload, and it is equally likely to be any two of the three. Finally, there is a 2% chance that all three substations experience an overload.

a) What is the probability that a blackout due to an overload occurs during a heat wave?

b) If a blackout occurred during a particular heat wave, what is the probability that the substation A alone experienced an overload?

c) If a blackout occurred during a particular heat wave, what is the probability that an overload occurred at two or more substations simultaneously?

Thank you!

Answer 1