A home security system may detect movement using its two different sensors. If motion is detected by any of the sensors, the system will alert the police. If there is movement outside, sensor V (video camera) will detect it with probability 0.95, and sensor L (laser) will detect it with probability 0.8. If there is no movement outside, sensor L will detect motion anyway with probability of 0.05, and sensor V will detect motion anyway with probability 0.1. Based on past history, the probability that there is movement at a given time is 0.7. Assume these sensors have proprietary algorithms, so that conditioned on there being movement (or not),the events of detecting motion (or not) for each sensor is independent.

(a) Given that there is movement outside and that sensor V does not detect motion, what is the probability that sensor L detects motion?

(b) Given that there is a moving object, what is the probability that the home security system alerts the police?

(c) What is the probability of a false alarm? That is, that there is no movement but the police are alerted anyway?

(d) What is the probability that there is a moving object given that both sensors detect motion?