A network intrusion software uses two systems to detect intruders. If an intruder is present, system A sounds the alarm 90% of the time, while system B sounds the alarm 95% of the time. If no intruder is present then system A sounds the alarm 20% of the time and system B only 10% of the time. You may assume that under a given condition (intruder present or not) the two systems operate independently
a) If there is an intruder, what is the probability that both systems sound an alarm?
b) If there is no intruder, what is the probability that both systems sound an alarm?
c) If there is an intruder, what is the probability that at least one of the alarms will sound?
d) A particular network has an intruder with 40% probability. Given that both alarms sound, what is the probability than an intruder is present in the network?