Measuring activity of uranium in a Geiger counter pulses arrive according to a Poisson process with rate 2 arrivals per second. Measured plutonium the arrival rate is 5 seconds.

For 0.2 seconds if there were no arrivals, what is the probability that uranium was being measured?

I think such problems can be solved with the Erlang distribution or truncated Poisson,

is this correct, or how they do it?

Thank you very much