In the Selected Answers section of a mathematics text, there are an average of 2 incorrect answers per 1000 questions. The probability that there are 15 incorrect answers in a set of 4000 questions is
A) $ e^{-2} 2^{8} / 8 $ !
B) $ e^{-8} 8^{15} / 15 $ !
C) $ e^{-4} 4^{2} / 2 ! $
D) $ \mathrm{e}^{-2} 8^{2} / 2 $ !

Question

In the Selected Answers section of a mathematics text, there are an average of 2 incorrect answers per 1000 questions. The probability that there are 15 incorrect answers in a set of 4000 questions is 
A) $ e^{-2} 2^{8} / 8 $ !
B) $ e^{-8} 8^{15} / 15 $ !
C) $ e^{-4} 4^{2} / 2 ! $
D) $ \mathrm{e}^{-2} 8^{2} / 2 $ !

Quizplus · Accepted Answer

The problem follows a Poisson distribution with a mean of 8 incorrect answers for 4000 questions. The probability of observing 15 incorrect answers is given by the Poisson probability formula: $ P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!} $, where $\lambda = 8$ and $k = 15$.

In the Selected Answers Section of a Mathematics Text, There e−228/8 e^{-2} 2^{8} / 8 e−228/8

In the Selected Answers Section of a Mathematics Text, There $e^{-2} 2^{8} / 8$