You are a physician . You think that one of your patients may have strep throat
ID: 2984525 • Letter: Y
Question
You are a physician . You think that one of your patients may have strep throat but you feel the chance is only 1/2 , so you take some swabs from the throat and send them to a lab for testing , to make sure . The test is not perfect . If the patient has strep throat , then 70% of the time the lab say YES , but 30 % of the time it says NO.If the patient does not have strep throat , then 90% of the time the lab say NO , but 10% of the time it says YES.You send five successive swabs from your patient and get back these results , in order : YES,NO,YES,NO,YES.Your friend says , "what a useless test", but you have thought about the probability .How does this information affect your estimate of your patient's condition?
Explanation / Answer
Probability of Yes is ( 0.7 + 0.1 )/2 = 0.4
Probability of NO is ( 0.3 + 0.9 )/2 = 0.6
But the actual probabilty of yes = 3/5 = 0.6 and no is 2/5 = 0.4, This indicates that the patient has strep throat as the probabiltiy is more skewed towards yes. If the P( strep throat ) = 0.5, then we expect yes only twice, but given that yes occured thrice P( strep throat ) > 0.5 and hence I believe that the patient has a strep throat
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