A Geiger counter counts the number of alpha particles from radioactive material. Over a long period of time, an average of 27 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 32 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 2 second period