According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?

13.53% probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

is the Euler number

is the mean in the given time interval.

According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years.

One earthquake each 100/5 = 20 years.

What is the probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years?

40 years, so

This probability is P(X = 0).

13.53% probability that no earthquakes with a magnitude of 6.5 or greater strike the San Francisco Bay Area in the next 40 years