Polygraph lie-detector machines are commonly used in criminal investigations. The

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