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.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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.
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 4 second period.
Transcribed Image Text: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. 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 4 second period.
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