Question

California is hit every year by approximately 500 earthquakes that are large enough to be felt. However, those of destructive magnitude occur, on the average, once a year. Find the probability that at least 3 months elapse before the first earthquake of destructive magnitude occurs.

Answer 1

A destructive earthquake happens once per year.

The exponential equation would be f(x) = 1-e^-x

The probability of going 3 months out of a year would be

P(X≥3/12)  ( divide 3 months by 12 months per year).

Now x equals 3/12

Now you have

P = 1-(1-e^-3/12)

= e^-1/4

= 0.7788

The probability that at least 3 months elapse would be 0.7788

(Round answer as needed).