In The Dark Knight, Batman relies on two independent informants to predict whether the Joker is planning an attack.
25% of the time, the Joker actually plans an attack.
Informant 1 correctly identifies an attack 80% of the time but also falsely reports an attack 15% of the time.
Informant 2 correctly identifies an attack 85% of the time but also falsely reports an attack 10% of the time.
Batman receives reports from both informants. If both informants report an attack, what is the probability that the Joker is actually planning one?