The Dark Knight: Predicting a Joker Attack with Multiple Informants

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?