(Solution) - Suppose the counts recorded by a Geiger counter follow a -(2025 Original AI-Free Solution)

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Suppose the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute.
(a) What is the probability that there are no counts in a 30- second interval?
(b) What is the probability that the first count occurs in less than 10 seconds?
(c) What is the probability that the first count occurs between 1 and 2 minutes after start-up?