Question

85% if suspect tried for terrorism 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 suspect of terrorism will confess after the prolongued question is 40% if the supect is innocent, and 10% if the suspect is guilty.
A Suspect. Josef K., is being tried for terrorism. If he confesses after prolonged questioning, what is the probability that he is actually guilty ? and how can you explain this puzzles result?

Answer 1

(first of all, you many need to explain the puzzle. then explain why it really make sense even though it seems to be puzzling).
Note you may use the contingency tables or any other method to find the probability in this problem.

Answer 2

sorry about this long question :(

Answer 3

\[\large P(guilty \cap confess)=0.85\times0.1=0.085\]
\[\large P(innocent \cap confess)=0.15\times0.4=0.060\]
The required probability is given by:
\[\large \frac{0.085}{0.085+0.060}=you\ can\ calculate\]

Answer 4

@kropot72 thank you so much that all or there is more for me to solver?

Answer 5

yes hes correct

Answer 6

@Andresfon12 You just need to do the following calculation to find the required probability:
\[\large P(guilty)=\frac{0.085}{(0.085+0.060)}=you\ can\ calculate\]

Answer 7

@kropot72 ok

Answer 8

You're welcome :)