Suppose the probability of a major earthquake on a given day is 1 out of 10,000.Use the Poisson model to approximate the probability that there will be at least one major earthquake in the next 2000 days.
A)0.1813
B)0.1637
C)0.8187
D)0.8363
E)0.0175

Question

Quizplus · Accepted Answer

The Poisson model can be used to approximate the probability of a given number of events happening in a fixed interval of time or space if these events happen with a known average rate and independently of the time since the last event. The average rate ($\lambda$) here is the expected number of earthquakes in 2000 days. Given the probability of an earthquake on any given day is $1/10,000$, for 2000 days, $\lambda = 2000 \times (1/10,000) = 0.2$. The probability of at least one earthquake is $1 - P(0)$, where $P(0) = e^{-\lambda} = e^{-0.2}$. Thus, $1 - P(0) = 1 - e^{-0.2} \approx 0.1813$.

Suppose the Probability of a Major Earthquake on a Given