Question

     (iii) 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

Poisson distribution

$P(X=x) = \frac{e^{-λ} \times λ^x }{x!} \\ λ=2 \\ x=5 \\ P(X=5) = \frac{e^{-2} \times 2^5 }{5!} \\ = 0.03609$