The number of bacterial colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 4 per cubic centimeter (cm3). (a) If five 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies. (Round your answer to four decimal places.) (b) How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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The number of bacterial colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 4 per cubic centimeter (cm3).
(a)
If five 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies. (Round your answer to four decimal places.)
 
(b)
How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony?
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