Particles are emitted by a radioactive source according to a Poisson process with rate λ = ln5 per hour. (a) What is the probability that during at least one of five consecutive hours no particles are...

Particles are emitted by a radioactive source according to a Poisson process with rate λ = ln5 per hour.

(a) What is the probability that during at least one of five consecutive hours no particles are emitted?

(b) Knowing that during a given hour two particles were emitted, what is the probability that one of them was emitted during the first half-hour and the other during the second half-hour of the hour in question?

(c) In (b), if we know that the first particle was emitted over the first half hour, what is the probability that the second particle was emitted during the first half-hour as well?