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When a saliva sample is collected from a patient to test for the presence of a...

When a saliva sample is collected from a patient to test for the presence of a new virus, occasionally the sample does not contain enough of the virus' genetic material to be viable for testing. Suppose the probability that any given sample is viable for testing is 0.27 and that the viability of a sample is independent from sample to sample. For a random selection of 12 saliva samples, given that more than 2 samples were found to be viable, find the probability that less than 4 samples were viable.

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