Question

Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative. Round to three decimal places as needed.

Positive Test Result
Negative Test Result
Subject has the disease
87
9
Subject does not have the disease
27
312

Answer 1

To calculate the conditional probability of having the disease given a negative test result, we divide the number of subjects who have the disease and tested negative by the total number of negative test results, then round the result to three decimal places.

Step-by-step explanation:

The question is about calculating the conditional probability that a subject has the disease given that the test result is negative. To find this, we use the formula for conditional probability which is P(A|B) = P(A and B) / P(B), where A is the event that the subject has the disease and B is the event that the test result is negative.

First, we add up the figures to get the total number of subjects who have the disease (87 + 9) and the total number of negative test results (9 + 312). Then, we calculate the conditional probability: P(A and B) is the subjects who have the disease and tested negative (9), P(B) is the total number of negative test results (9 + 312).

The probability that the subject has the disease given that the test result is negative will be P(A|B) = 9 / (9 + 312). After performing the calculation and rounding to three decimal places as needed, we can provide the precise answer.