Scanning technology is used at an airport to determine whether passengers are carrying any illegal items. An alarm will activate if the scanning technology detects an illegal item. It is estimated that 1% of passengers are carrying illegal items. The alarm activates 98% of the time when a person has an illegal item and 5% of the time when a person does not have an illegal item. 1. Define the events in the problem. 2. State the known probabilities in the problem (use probability notation and the events defined in Q1). 3. What is the probability that the alarm activates for a random person? 4. What is the probability that a person is carrying an illegal item given the alarm activates? 5. What is the probability that a person is carrying an illegal item given the alarm does not activate?