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#1




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. 10.05 multiplied by 8 B. 0.05 multiplied by 8 C. 0.05 power of 8 D. 0.95 power of 8 E. 10.95 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 
#2




Each time the test is performed, there is a 0.95 (95%) probability that it will give a truenegative 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: 1Probability (all negative) =1(0.95^8) 
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#3




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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