Probability problem: about a radioactive substance A substance undergoes radioactive decay by emitting particles at random times. Observation shows that the probability of an emission is proportional to the observation time, in the limit of small observation times. Suppose that empirical data show that the substance emits $200$ particles per minute, on the average. What is the probability that a $1$-minute count will be exactly $200$? thanks :)

I think that you need to use the Poisson distribution.

!Poisson distribution

If I am correct, then $λ$ is the expected value, which is $200$. The number $k$ is the actual number of observations, which is also $200$.

The above formula should give the probability that you will observe exactly $200$ particles.