Question

1. Three towns, A, B, and C, have a funny arrangement with respect to the power grid. They all get their power from a single hydraulic power plant up the river. Both cities A and B each have power lines that supply power directly from the plant. Furthermore, there is a supply line between A and B, so that either city will not lose power in the case that one of their direct lines from the plant fails. (Of course, if both lines fail, then both cities lose power.) City C, really a suburb of city B, has one single power supply line and it comes directly from city B.
   
   However, all of the power lines in the system are aging now, and any one of the lines has a 20% chance of failing on any particular day. (This obviously puts city C in the poorest of circumstances.) What is the empirical probability that city C will have power on any particular day? Estimate this over 2000 “particular days”?

Answer 1

the probability that the line fails on any particular day is 0.20. We will use 1 to indicate that a line to a city is working and 0 to indicate that it has failed.

To simulate this we use the following steps

• generate a random number from uniform distribution in the interval (0,1) using RAND()
• If the random number generated is less than 0.20 the that particular line is down, else it is up.

The city C has power if

• The lines from the power plant to B and from B to C are up (column C+column E =2, then C has power)
• or
• The line from the power plant to A, from A to B and from B to C are up (column B+column D+column E =3, then C has power)

Prepare the following sheet

copy the rows to make 2000 rows each row indicating if city C has power on that particular day.

Paste these as values to avoid changes

get this

where 1 in the last column, Power to C indicates that the city C has power on a particular day of the simulation.

Now we calculate the empirical probability that city C will have power on any particular day as

Add this to the sheet

get this

ans: the empirical probability that city C will have power on any particular day is 0.732