Testing for a disease can be made more efficient by combining samples. If the samples from four people are combined and the mixture tests negative, then all four samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.1, find the probability of a positive result for four samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary? The probability of a positive test result is (Round to three decimal places as needed.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter6: Ratio, Proportion, And Probability
Section6.7: Probability And Odds
Problem 2E
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Testing for a disease can be made more efficient by combining samples. If the samples from four people are combined and the mixture tests negative, then all four samples are negative. On the
other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.1, find the probability
of a positive result for four samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
The probability of a positive test result is
(Round to three decimal places as needed.)
Transcribed Image Text:Testing for a disease can be made more efficient by combining samples. If the samples from four people are combined and the mixture tests negative, then all four samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.1, find the probability of a positive result for four samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary? The probability of a positive test result is (Round to three decimal places as needed.)
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