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The test to detect the presence of strep throat is 98% accurate for a person who has a disease and 97% accurate for person who does not have the disease. If 3.5% of the people in a given population actually have strep throat, what is the probability that a randomly chosen person test positive?

User Welton
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1 vote

Answer:

The probability that a randomly chosen person test positive is 0.06325

Explanation:

Let T denotes the test and D denotes the disease

We are given that The test to detect the presence of strep throat is 98% accurate for a person who has a disease


P(T|D)=0.98

We are also given that 97% accurate for person who does not have the disease.

So,
P(T^C|D^C)=0.97

Now we are given that 3.5% of the people in a given population actually have strep throat,

So,P(D)=0.035


P(T)=P(T|D)P(D)+P(T|D^C)P(D^C)


P(D)=P(T|D)P(D)+P(T^C|D)P(D)


\Rightarrow P(T^C|D)=1-P(T|D)

Now we find :


P(T)=P(T|D)P(D)+(1-P(T^C|D^C))(1-P(D))


P(T)=0.98 * 0.035+(1-0.97)(1-0.035)=0.06325

Hence the probability that a randomly chosen person test positive is 0.06325

User Thach Van
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