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

Answer:

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

Step-by-step 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:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{n(A\cap B)}{n(B)}$

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:

$P(A|B)=\frac{n(A\cap B)}{n(B)}$

            $=\frac{137}{153}$

            $=0.8954$

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