Question

In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.62.

What is the probability of more than one death in a corps in a year?

Answer 1

To find the probability of more than one death in a corps in a year, we can use the Poisson distribution. The mean number of soldiers killed by horse kicks in a corps in a year is 0.62. Using the Poisson probability formula, we can calculate the probability of exactly one death and subtract it from 1 to find the probability of more than one death.

Step-by-step explanation:

To find the probability of more than one death in a corps in a year, we need to use the Poisson distribution. The Poisson distribution gives us the probability of a certain number of events occurring in a fixed interval of time or space, when the events are independent and the average rate of the events is known. In this case, the mean number of soldiers killed by horse kicks in a corps in a year is 0.62.

To find the probability of more than one death, we need to calculate the probability of exactly one death and subtract it from 1. The probability of exactly one death can be calculated using the Poisson probability formula: P(X = k) = (e^-λ * λ^k) / k!, where λ is the mean and k is the number of deaths.

Let's calculate it:

1. P(X = 1) = (e^-0.62 * 0.62^1) / 1! = 0.4853
2. P(more than 1 death) = 1 - P(X = 1) = 1 - 0.4853 = 0.5147

Therefore, the probability of more than one death in a corps in a year is approximately 0.5147, or 51.47%.