math 123 help please

Question

Polygraph tests have an accuracy rate of about 85%. this means that it detect 85% of people who lie and 85% of people who are telling the truth.

A company of 6000 employees has everyone submit to a polygraph test. It turns out there are 60 employees who will lie during their polygraph. If someone does not pass their polygraph test, what is the probability they lied?

Answer 1

Hi Sandyi,

This problem is best solved with a tree diagram. Unfortunately, it doesn't look like I can post a picture here, but we could certainly walk through one in a lesson. I will try my best to explain it with words here though. So, from the start, you are given that (6000-60) = 5940 employees will tell the truth, while 60 employees will lie during their polygraph. Of those 5940 who tell the truth, 85% of them (5940*0.85 = 5049) will be found to have told the truth because the polygraph has 85% accuracy. However, 15% of them (5940*0.15 = 891) will be found to have lied because the polygraph is wrong (100% - 85% = 15%) of the time.

On the other side, 60*0.85 = 51 employees who lied will be found to have lied because the polygraph has 85% accuracy. The other 9 employees will have lied but will be found to have been telling the truth because the polygraph is wrong 15% of the time.

Thus, the total population of employees that failed the polygraph is 891 + 51 = 942 employees. This problem really boils down to a conditional probability. Thus, we want to take the employees who both did not pass their polygraph test and lied and divide it by the total number of employees that did not pass their polygraph test.

That being said, the final answer comes out to be 51/942 = 0.0541.

Please let me know if you would like further explanation for this problem or other problems from your course in a lesson. I'd be happy to help!

Regards,

Danny