Question

The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.

Answer 1

To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:

P(positive|disease) = P(positive and disease) / P(disease)

From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.

We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.

Substituting these values into the formula, we get:

• P(positive|disease) = 136 / 144

Simplifying, we get:

• P(positive|disease) = 0.944

Rounding to three decimal places, we get:

• P(positive|disease) ≈ 0.944

Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.