4.5% of a population are infected with a certain disease.There is a test for the disease,however the test is not completely accurate.94% of those who have the disease will test positive.However 3.7% of those who do not have the disease will also test positive (false positives).What is the probability that any given person will test positive? Round your answer to three decimal places if necessary.
A)0.94
B)0.042
C)0.078
D)0.035
E)0.489

Question

Quizplus · Accepted Answer

We need to use Bayes' theorem to calculate the probability that any given person will test positive:
P(disease|positive) = P(positive|disease) * P(disease) / P(positive)
where P(disease) = 0.045 (given), P(positive|disease) = 0.94 (given), and we need to calculate P(positive). 
To calculate P(positive), we need to consider both true positives and false positives:
P(positive) = P(positive|disease) * P(disease) + P(positive|no disease) * P(no disease)
= 0.94 * 0.045 + 0.037 * (1 - 0.045) 
= 0.04443
Now we can calculate P(disease|positive):
P(disease|positive) = 0.94 * 0.045 / 0.04443
= 0.952
Therefore, the probability that any given person will test positive is 0.078 (rounded to three decimal places), so the best choice is C.

45% of a Population Are Infected with a Certain Disease