Question

Kevin’s family has a history of diabetes. The probability that Kevin would inherit this disease is 0.75. Kevin decides to take a test to check if he has the disease. The accuracy of this test is 0.85.
We now know that the test predicted that Kevin does not have the disease. Using this information, calculate the probability that Kevin does not have diabetes after the test was taken.
A. 0.0925
B. 0.3565
C. 0.4827
D. 0.6538
E. 0.8765

Answer 1

Step-by-step Answer:

We will solve the problem as follows:

Let

K=event that Keven has the disease

k=event that Kevin does not have the disease

T=event that test is accurate.

t=event that test is not accurate

We assume the events K and T are independent.

P(K)=0.75

P(k)=1-0.75=0.25

P(T)=0.85

P(t)=1-0.85=0.15

Since we know that the results of the test is negative, it can come from two possible cases:

P(K and t)=P(K)*P(t)=0.75*0.15=0.1125   (Kevin has disease, test inaccurate)

P(k and T)=P(k)*P(T)=0.25*0.85=0.2125  (Kevin does not have disease, test accurate)

Probability of negative result

= P(K and t) + P(k and T) = 0.1125+0.2125 = 0.325

Probability that Kevin does not have disease, given negative test, i.e. test accurate:

= P(k and T) / [P(K and t) + P(k and T)]

= 0.2125 / 0.325

= 0.6538