You are a physician You think that one of your patients may

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 says YES, but 30% of the time it says NO. If the patient does not have strep throat, then 90 % of the time the lab says NO , but 10% of the time it says YES. You send five successive swabs from your patients and get back these results in order: YES,NO,YES,NO,YES. Your friend says, \" What a useless test\", but you` ve thought about probability. How does this information from the lab affect your estimate of your patient`s condition?

Solution

Prob for strep throat = 0.5

Lab test Yes NO

Has strep 80% 20%

no strep 10% 90%

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Results are yes, no, yes, no, yes

Hence prob for having strep if result is yes =8/9

prob for having strep, if result is no = 9/11

Hence out of 5, we have prob for strep throat as = 1/5 (8/9*3 +9/11*2)

= 1/5(24/9+18/11)

=0.3757

As I get some idea about 37% prob test is not fully usefless.