Question

There are 3 servers: A, B, and C. They occasionally crash, independent of each other. Each week server A has a 9% chance of crashing, server B has a 12% chance of crashing, and server C has a 14% chance of crashing.

What is the probability that:

1.) There are no crashes this week?

2.) There is exactly one crash this week?

3.) There are one or more crashes this week?

Answer 1

a)

P(No crash) = P(A) * P(no crash) + P(B) * P(no crash) + P(C) * P(no crash)

= 1/ 3 * (1 - 0.09) + 1 / 3 * ( 1 - 0.12) + 1/3 ( 1 - 0.14)

= 0.8833

b)

P(Exactly one crash) = P(A) * P(crash) + P(B) * P(no crash) + P(C) * P(no crash) +

P(A) * P(no crash) + P(B) * P(crash) + P(C) * P(no crash) + P(A) * P(no crash) + P(C) * P(no crash) + P(C) * P(no crash)

= 1/ 3 * (0.09) + 1 / 3 * ( 1 - 0.12) + 1/3 ( 1 - 0.14) +1/ 3 * (1 - 0.09) + 1 / 3 * (0.12) + 1/3 ( 1 - 0.14)

+1/ 3 * (1 - 0.09) + 1 / 3 * ( 1 - 0.12) + 1/3 ( 0.14)

= 0.9664

c)

P( one or more crashes) = 1 - P( no crash)

= 1 - 0.8833

= 0.1167