Probability of the correct diagnosis in a lie detector

#1
Probability of the correct diagnosis in a lie detector
A lie detector correctly diagnoses 90% of those who lie (M) and 95% of those who do not lie. A person is chosen at random from a group of 100 people from which 20 are known to lie. Whether that person lies or not, what is the probability that the detector will provide a correct diagnosis?
 

rogojel

TS Contributor
#2
If I understand the question correctly you need to apply the total probability formula:

P(G)=P(G|A1)*P(A1)+P(G|A2)*P(A2) where A1 and A2 are the events that the subject lied respectively that he did not lie.

good luck