Question

Suppose a county’s recent health report gives a pet allergy prevalence of 0.13 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 0.06. The probability that the test gives a negative result when a child really does have a pet allergy is 0.12. The tree 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.

Answer 1

Answer: To calculate the probability of an incorrect test result, we need to consider two cases:

1. The test gives a positive result when the child does not have a pet allergy (false positive).

2. The test gives a negative result when the child does have a pet allergy (false negative).

The probability of a false positive is given as 0.06, which means that out of 100 children who do not have a pet allergy, 6 will test positive for it. The probability of a false negative is given as 0.12, which means that out of 100 children who do have a pet allergy, 12 will test negative for it.

To calculate the probability of an incorrect test result, we can add the probabilities of these two cases:

Probability of incorrect test result = Probability of false positive + Probability of false negative

Probability of incorrect test result = 0.06 + 0.12

Probability of incorrect test result = 0.18

Therefore, the probability of an incorrect test result is 0.18, or 18% (rounded to two decimal places).