We are told that there is a 72% chance that the test will catch a person who is actually lying. In other words, the probability that the machine indicates the person is lying, given that the person is lying, is 0.72. So, we have the following.

P(L|T^C) =

Additionally, we are given that there is a 7% chance that the machine will falsely accuse someone of lying. In other words, the probability that the machine indicates that the person is lying, given that they are actually telling the truth, is 0.07. So, we have the following.

P(L|T) =