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 tests positivepositive​, given that he or she hadhad the disease.

Answer 1

The probability of getting someone who tests positive​, given that he or she had the disease is 0.8954.

Explanation:

The data provided is:

YES NO Total

Positive 137 8 145

Negative 16 139 155

Total 153 147 300

An individual is selected at random from the group.

We need to compute the probability of getting someone who tests positive​, given that he or she had the disease.

The conditional probability of an event A given that another event B has already occurred is:

`P(A|B)=(P(A\cap B))/(P(B))=(n(A\cap B))/(n(B))`

Let A = individuals who tests positive and B = individual who had the disease.

The number of individuals who tests positive and had the disease is,

n (A ∩ B) = 137

n (B) = 153

Compute the conditional probability of A given B as follows:

`P(A|B)=(n(A\cap B))/(n(B))`

`=(137)/(153)`

`=0.8954`

Thus, the probability of getting someone who tests positive​, given that he or she had the disease is 0.8954.