Question

A rainstorm in Portland, Oregon, has wiped out the electricity in about 7% of the households in the city. A management team in Portland has a big mecting 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 loot electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households. Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Answer 1

The probability that all six team members in Portland have not lost electricity is found by multiplying the probability of a single household having power (93%) to the power of six, the number of households.

Step-by-step explanation:

The probability that none of the six team members in Portland has lost electricity can be calculated by using the complementary probability of a single household losing power. Since each case is independent, the combined probability can be found by multiplying together the probability that each household has power.

Given that there's a 7% chance a household has lost power, this means there is a 93% chance a household has not lost power (100% - 7% = 93%). Therefore, the probability that all six households have electricity is:

0.93 (probability one household has power) ^ 6 (number of households) = probability all six households have power.