Question

according to u s government statistics, mononucleosis (mono) is four times more common among college students than the rest of the population. blood tests for the disease are not 100% accurate assume that the following table of data was obtained regarding students who came to a certain schools health center complaining of tiredness, a sore throat, and slight fever. if a student is selected from this group, find the probability that the test is negative, given that the student doesnt have mono. the probability is □. (type an integer or decimal rounded to three decimal places as needed)

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of a two - way table, if \(A\) is the event of a negative test and \(B\) is the event of not having mono, then \(P(A|B)=\frac{\text{Number of students with negative test and no mono}}{\text{Number of students with no mono}}\).

Step2: Identify the values from the table

From the table, the number of students with a negative test and no mono is \(17\), and the number of students with no mono is \(42\).

Step3: Calculate the probability

\(P=\frac{17}{42}\approx0.405\)

Answer:

\(0.405\)