Smoke detector and probability
In a certain town 63% of the houses have smoke detectors. The fire brigade estimates that people die 24% of the time when the fire is in a house without a smoke detector, but only 13% of the time when there is a smoke detector. In addition 31% of callouts are false alarms that do not involve a fire. What is the probability that if the fire brigade has a callout then they will be fighting a fire in which someone will die?