Suppose you are planning to study the respiratory physiology of the common toado, Tetractenos hamiltoni, a small fish found in tidal pools. Unknown to you, the pool from which you decide to collect specimens has 25 individuals, 5 of which have a fungal infection in their gills that may confound the experiment you plan to run. (a) What is the probability that you collect 10 fish from this pool and none have infected gills? (b) What is the probability that you collect 10 fish and half have infected gills? Show your work.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Suppose you are planning to study the respiratory physiology of the common toado, Tetractenos hamiltoni, a small fish found in tidal pools. Unknown to you, the pool from which you decide to collect specimens has 25 individuals, 5 of which have a fungal infection in their gills that may confound the experiment you plan to run.
(a) What is the probability that you collect 10 fish from this pool and none have infected gills?
(b) What is the probability that you collect 10 fish and half have infected gills? Show your work.
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