Question

A power system will collapse if a ground fault occurs on any two of lines A, B, and C simultaneously. Assume that ground faults on lines A, B, and C are independent and have identical probability of 0.01. Hint: parts (a) and (b), use Bernoulli Trials; part (c), use Bayes Rule. a) What is the probability that the system will collapse

Answer 1

0.000298 = 0.0298% probability that the system will collapse

Explanation:

Number of possible ways the system can fail:

2 lines from a set of 3 fail, or all three fail.

Two from a set of 3:

Can be A and B, A and C, or B and C. Three possible outcomes then.

The probability of each is:

0.01*0.01*0.99

Two failling, each with 0.01 probability, and 1 working, with 0.99 probability.

All three:

Each with 0.01 probability.

a) What is the probability that the system will collapse

Both cases, so

`p = 3*(0.01)^2*0.99 + (0.01)^3 = 0.000298`

0.000298 = 0.0298% probability that the system will collapse