Question

A rainstorm in Portland, Oregon, has wiped out the electricity in about 10% of the households in the city. A management team in Portland has a big meeting tomorrow, and all 6 members of the team are hard at work in their separate households, preparing their presentations. What is the probability that none of them has lost electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households.

Answer 1

The probability that a given household has lost electricity is 10%, or 0.1. So the probability that a given household has not lost electricity is 1 - 0.1 = 0.9.

Since the loss of electricity is independent among the households of the management team, we can find the probability that none of them has lost electricity by multiplying the probability of no loss in any one household (0.9) by itself 6 times, since there are 6 members of the team:

0.9 * 0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.54

So the probability that none of the management team members has lost electricity in his or her household is 54%.