Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power. Yet Ames took routine lie detector tests and each time passed them. How can this be done? Recognising control questions, employing unusual breathing patterns, bitting one's tongue at the right time, pressing one's toes hard to the floor, and counting backward by 7 are countermeasures that are difficult to detect but can change the results of a polygraph examination (Source: Lies! Lies! Lies! The psychology of deceit, by C.V. Ford, professor of psychiatry, University of Alabama) In fact, it is reported by professor Ford's book that after 20 minutes of instruction, a 85% of those trained in such techniques, are able to pass the polygraph examinationeven when guilty of crime. Suppose that a random sample of 9 students are told a secret and then given instructions on how o pass the polygraph examination without revealing their knowledge of the secret.

What is the probability that all the students are able to pass the polygraph examination?

Guest Apr 3, 2017

#1**+1 **

University of Alabama???? Roll Tide !!!

Sorry I just had to say that...I don't really know how to do this...

This reminded me of an episode of Mythbusters that I watched where they tested different methods of " cheating " a lie detector test, and I don't think any of them really worked. But I don't remember very well...

But I'm pretty sure that question is basically just this:

There are 100 people in a room. 15 of them have on a yellow shirt. 85 of them have on a blue shirt. You randomly select 9 people. What is the probability that all 9 of those people have on a blue shirt?

hectictar
Apr 3, 2017

#2**+1 **

Okay, I'm really bad at probabilities but I will try it...

I will use the question I said just because it's easier.

Also, I think I should have said that each time you take one person out of the room, a new person comes into the room.

If you don't replace the person you took out, then it changes the answer.

SO

Probability of first person to have on a blue shirt: 85/100

Probability of second person to have on a blue shirt: 85/100

Probability of third person to have on a blue shirt: 85/100

...and so on...

Multiply all the probabilities together:

\(\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100}*\frac{85}{100} \\~\\ =(\frac{85}{100})^9 \\~\\ \approx 0.2316\)

So about a 23.16 % chance.

I know this is probably the worst way of doing it but I tried...

hectictar
Apr 3, 2017