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Old 03-04-2016
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Angry probability question

a new serologic test for detecting prostate cancer is NEGATIVE in 95% of patients who do not have disease. if the test is used in 8 consecutive blood samples taken from patients without the disease, what is the probability of getting at least one positive test result?

A. 1-0.05 multiplied by 8
B. 0.05 multiplied by 8
C. 0.05 power of 8
D. 0.95 power of 8
E. 1-0.95 power of 8

guys answer is E and i know how to calculate probability. i am just not understanding why there is 1- probability of all negatives. where 1 came from. anyone plz
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  #2  
Old 03-13-2016
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Each time the test is performed, there is a 0.95 (95%) probability that it will give a true-negative result and 0.05 (5%) probability it will give a false positive result.

To calculate change of all tests being negative, use multiplication rule for independent events:

Probability (all negative) = 0.95^8



total probability is always equal to 1.0 (1005). So probability that at least one test turns out positive is:

1-Probability (all negative)
=1-(0.95^8)
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Old 03-14-2016
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The specificity of the test of the test (i.e., true negative rate) is 95%, but what you need is the false positive rate. In order to get the false positive rate, you need to subtract 1 by the specificity. The probability of getting a false positive is the false positive rate to the power of the number of consecutive samples.
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