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. the individual actually had the disease yes no positive 140 27 negative 8 125 the probability is approximately □. (round to three decimal places as needed.)

Explanation:

Step1: Identify relevant values

We want the probability of positive - test given the person has the disease. The number of people who have the disease and tested positive is 140, and the total number of people who have the disease is \(140 + 8=148\).

Step2: Calculate the conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of frequency - based probability, if \(A\) is the event of testing positive and \(B\) is the event of having the disease, the probability \(P(\text{positive}|\text{had disease})=\frac{\text{Number of positive and had disease}}{\text{Number of had disease}}\). So \(P=\frac{140}{148}\).

Step3: Simplify and round

\(\frac{140}{148}\approx0.946\)

Answer:

0.946