Question

During a laboratory experiment, the average number of radioactive particles passing through   a counter in 1 millisecond is 2. What is the probability that 5 particles enter the counter in any given millisecond?                                                                                                       

Answer 1

Assume that the particle stream is the easiest.

Then the number $\xi$ of radioactive particles passing through a counter in 1 millisecond has the Poisson's distribution, i.e.

$P(\xi =k)=\dfrac{\lambda^k}{k!}e^{- \lambda}$ where k = 0,1,2,.... and by hypothesis $\lambda = 2$. So,

$P(\xi=5)=\dfrac{2^5}{5!}e^{-2}\approx 0.036$