A small store installed a diesel-powered generator for emergency power outage because they function independently of electric power. The past history of the town indicates that on about 5% of days during summer the town loses electricity due to high winds. However, high winds do not affect functioning of genera- tors. These generators have a failure rate of about 2%. On a given summer day, what is the probability that the store will be totally out of power?
please answer
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.05 * .02 = ?
To calculate the probability that the store will be totally out of power on a given summer day, we need to consider the probabilities of both the town losing electricity and the generator failing.
First, let's calculate the probability of the town losing electricity due to high winds. We are given that on about 5% of days during summer, the town loses electricity. Therefore, the probability of the town losing electricity is 0.05, or 5% (since probability is expressed as a decimal or fraction).
Next, let's calculate the probability of the generator failing. We are given that the generator has a failure rate of about 2%. Therefore, the probability of the generator failing is 0.02, or 2%.
Since the generator functions independently of electric power, the town losing electricity and the generator failing are two separate events. To calculate the probability of both events occurring, we multiply the probabilities together.
Probability of the store being totally out of power = Probability of the town losing electricity * Probability of the generator failing
= 0.05 * 0.02
= 0.001
Therefore, the probability that the store will be totally out of power on a given summer day is 0.001, or 0.1%.