In this example doctors developed a new strep throat and administered it to 100
ID: 3225613 • Letter: I
Question
In this example doctors developed a new strep throat and administered it to 100 patients with a certain set of symptoms. 80 of their patients definitely had strep throat whereas 20 did not. The test correctly identified strep throat in 76 of the 80 patients had it. The test incorrectly identified strep in 3 of the 20 who did not have it. The results of the study are summarized below.
a) using the above table find the probability that a randomly selected patient with this specific set of symptoms has strep throat b) using the above table find the probability that a randomly selected patient with the specific set of symptoms has a strept throat and tests positive. c) find the probability that a random selected patient with this specific set of stymptoms has a strep throat given that they test positive. d) find the probability that a randomly selected patient with this specific set of symptoms tests negative given that they dont have strep throat. e) find the probability that a randomly selected patient with the specific set of symptoms does not have strep throat or tests positive. f) are the events having strep throat and testing negative mutually exclusive.
have strep throat don't have strep throat totals test positive-- 76 3 79 test negative-- 4 17 21 totals-- 80 20 100Explanation / Answer
a)probability that a randomly selected patient with this specific set of symptoms has strep throat =80/100=0.8
b) probability that a randomly selected patient with the specific set of symptoms has a strept throat and tests positive
=76/100=0.76
c)probability that a random selected patient with this specific set of stymptoms has a strep throat given that they test positive =76/79 =0.9620
d)=17/20=0.85
e)=(76+3+17)/100=0.96
f)No; as they share some common patients
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