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 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

Answer 1

0.647 = 64.7% probability that none of them has lost electricity in his/her household

Explanation:

For each household, there are only two possible outcomes. Either they lost electricity, or they did not. The probability of a household losing electricity is independent of any other household. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

A rainstorm in Portland, Oregon, has wiped out the electricity in about 7% of the households in the city.

This means that
`p = 0.07`

6 members

This means that
`n = 6`

What is the probability that none of them has lost electricity in his/her household?

This is P(X = 0). So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(6,0).(0.07)^(0).(0.93)^(6) = 0.647`

0.647 = 64.7% probability that none of them has lost electricity in his/her household