Question

85% of suspects tried for terrorism actually are guilty. (Don’t worry about how we know this, just take
it as a fact for the sake of this problem.) Also, the probability that a person suspected of terrorism will
confess after prolonged questioning is 40% if the suspect is innocent, and 10% if the suspect is guilty.
A suspect, Josef K., is being tried for terrorism. If he confessed after prolonged questioning, what is the
probability that he is actually guilty? And how can you explain this puzzling result? (First of all, you
may need to explain why it is puzzling

Answer 1

The probability of a confession is given by:
\[\large P(confession)=P(guilty \cap confess)+P(innocent \cap confess)=\]
0.085 + 0.06 = 0.145
The probability of a confession and being actually guilty is given by:
\[\large \frac{P(guilty \cap confess)}{P(confess)}=\frac{0.085}{0.145}=you\ can\ calculate\]

Answer 2

Why is it puzzling?

Answer 3

Thanks alot for your answer!

Answer 4

@pty507 What steps can you not understand?