Suppose a county\'s recent health report gives a pet allergy prevalence of statu

Question

Suppose a county's recent health report gives a pet allergy prevalence of status 0.16 for kids. There is a new at-home test kit for pet allergies on the market that provides families with a convenient way to test if children have a pet allergy. The probability that the test gives a positive result when a child really does not have a pet allergy is 0.04. The probability that the test gives a negative result when a child really does have a pet allergy is 0.15. The tree 0.16 diagram shows the possible outcomes with the associated probabilities. What is the probability of an incorrect test result? Give your answer as a decimal precise to two decimal places.

Explanation / Answer

From the tree diagram , the two incorrect results are

P(Negative | Pet allergy) = 0.15

P(Positive|No pet allergy) = 0.04

Since above two events are mutually exclusive so

P(incorrect result) = P(Negative | Pet allergy) P(Pet allergy) +P(Positive|No pet allergy) P(no pet allergy)= 0.15*0.16+0.04*0.84= 0.06

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