A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 15 particles per minute occurs. Assume the arrival of particles at the counter follows a Poisson distribution. Round your answers to four decimals.

a) Find the probability of exactly 20 particles arrive in a particular one minute period.

b) Find the probability of exactly one particle arrives in a particular one second period.

c) Find the probability that at least one particle arrives in a particular one second period. 

d) Find the probability that at least two particles arrive in a particular 5 second period.