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 more than two earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next 40 years?
A) 0.1353
B) 0.2706
C) 0.3233
D) 0.8754

Question

Quizplus · Accepted Answer

The probability of more than two earthquakes in the next 40 years can be calculated using the Poisson distribution formula, where the average rate ($\lambda$) of events (earthquakes) in a given time period needs to be determined first. Given that there are 5 earthquakes every 100 years, the rate for 40 years is $5 \times \frac{40}{100} = 2$. The probability of having more than two earthquakes is the complement of the probability of having 0, 1, or 2 earthquakes. Using the Poisson formula $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, we calculate the probabilities for 0, 1, and 2 earthquakes and subtract their sum from 1. The correct calculation aligns with option C, indicating it accounts for the complement of the probabilities of having 0, 1, or 2 earthquakes in the given period.

According to Geologists, the San Francisco Bay Area Experiences Five