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 negative, given that he or she had the disease.
the individual actually had the disease

	yes	no
negative	5	128

the probability is approximately (round to three decimal places as needed.)

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event of testing negative and $B$ be the event of having the disease. Then $P(A|B)=\frac{\text{Number of people who had the disease and tested negative}}{\text{Number of people who had the disease}}$.

Step2: Identify relevant numbers from the table

The number of people who had the disease and tested negative is 5. The number of people who had the disease is $135 + 5=140$.

Step3: Calculate the probability

$P(A|B)=\frac{5}{140}\approx0.036$

Answer:

$0.036$