Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i. e., 92% sensi - tivity) and a 94% chance of correctly indicating that the disease is absent if the person really does not have the disease (i. e., 94% specificity). Suppose 10% of the popu - lation has the disease. (a) What is the probability that a randomly chosen per - son will test positive

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Mathematics

Isabelle

24 February, 23:21

Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i. e., 92% sensi - tivity) and a 94% chance of correctly indicating that the disease is absent if the person really does not have the disease (i. e., 94% specificity). Suppose 10% of the popu - lation has the disease. (a) What is the probability that a randomly chosen per - son will test positive

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Giovanni Norris · Answer 1

14.6% probability that a randomly chosen person will test positive

Step-by-step explanation:

We have these following probabilities:

10% probability that a randomly selected person has the disease.

If a person has the disease, 92% probability of testing positive.

100-10 = 90% probability that a person does not have the disease.

If a person does not have the disease, 100-94 = 6% probability of testing positive.

What is the probability that a randomly chosen person will test positive

92% of 10% or 6% of 90%.

Then

p = 0.92*0.1 + 0.06*0.9 = 0.146

14.6% probability that a randomly chosen person will test positive