Ex:            Consider a lie detector test. Notation for this problem is as follows:

− ≡ detector says you Lied

+ ≡ detector says you told the Truth

L ≡ you did Lie

T ≡ you told the Truth

The following information is given:

P( − | L ) = 0.89

P( + | L ) = 0.11

P( − | T ) = 0.1

P( + | T ) = 0.9

Determine the probability, P( L | − ), that you actually lied if the lie detector result says you lied. Our intuition might suggest an answer of approximately 90 %.

Sol'n:       Using Bayes' Theorem, we calculate the probability:

where

We need to know P(L) and P(T) to solve this problem.

Suppose we have the following additional information:

These values suggest that most people tell the truth. Using these values, we complete the calculation of the desired probability:

There is only a 32 % chance you lied when the detector says you lied.