Question

On average there are 3 earthquakes each year in a certain geographic location. The distribution of earthquakes in this geographic location obeys a poisson process. Calculate the probability there is 0

Answer 1

The probability of 0 earthquakes occurring in a certain geographic location is approximately e^(-3) or about 0.0498.

Step-by-step explanation:

To calculate the probability of 0 earthquakes occurring in a certain geographic location, we can use the Poisson distribution formula. The formula is:

P(X = k) = e^(-λ) * (λ^k) / k!

Where λ is the average number of earthquakes per year. In this case, λ = 3. To calculate the probability of 0 earthquakes occurring in a year, we substitute k = 0 in the formula:

P(X = 0) = e^(-3) * (3^0) / 0! = e^(-3) * 1 / 1 = e^(-3)

Therefore, the probability of 0 earthquakes occurring in a certain geographic location is approximately e^(-3) or about 0.0498.