0.5645
This means a person telling the truth is flagged as a liar 56.45% of the time. No, Polygraph lie detector machines do not work as this is too much a statistic for the innocent.
Step-by-step explanation:
Liars are identified 90% of the time.
Truth tellers are identified as truth tellers 50% of the time.
Out of 1000 Criminals, 700 criminals are telling the truth
Meaning 300 criminals are lying
Of the 700 truth tellers, the machine gets
it right 50% of the time
Meaning 350 positive results and 350 negative results.
Of the 300 liars, the machine gives a positive result 90% of the time.
Positive result = 0.9 × 300 = 270
Negative result = 0.1 × 300 = 30
The table of results is presented in the second attached image
The probability that a person is telling the truth given that the lie detector test has a positive result
The lie detector test gives a positive result 620 times
A person is telling the truth and the result gives a positive result 350 times.
Probability that a person is telling the truth given that the result is positive = (probability that a person is telling the truth and the machine gives a positive result)/(total number of positive results that the machine gives) = (350/620) = 0.5645