Answer to Question #119333 in Statistics and Probability for King

Question

The mean number of errors due to a bug occurring in a minute is 0.0001. What is the
probability that no error will occur in 20 minutes

Answer 1

Here we can use a Poisson Distribution with mean $m=0.0001$ in a minute.

$\therefore$ for no error in 20 minutes equivalent $m=20(0.0001)$

$=$ $0.002$

now Poisson distribution says

$P(X=x) = e\raisebox{0.25em}{-m} * \frac{m^x}{x!}$

therefore in order to find the probability no error will occur in 20 minutes we put $x=0.$

$P(X=0)= e\raisebox{0.25em}{-0.002}*\frac{(0.002)^0}{0!}$

$= 0.998*1$

$=0.998$

Answer : 0.998