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
