An airline security director has been advised that airline gate agents are constantly being interrupted while waiting on passengers by persons who accidentally bump alarms attached to the panic bars on exit doors in the gate area. For example, during the boarding process, if a child or careless adult touches one of the doors leading out to the airplane ramp, the alarm sounds. Consequently, the agent must respond by securing his position, perhaps in the face of a long line of passengers, go to the door where the alarm is sounding, and reset it with a key. The door need not be opened to sound an alarm; it just needs to be touched.

To combat this problem, the security director considers the purchase of a new sensor for the doors. However, he has some misgivings about the new equipment, and not to mention significant budget constraints. Based on his judgment, the security director estimates the odds of reducing false alarms given purchase of the new sensors is 2:1. Moreover, the odds that false alarms are not reduced (by other means) given that the old sensors are kept were assessed to be 3:1. Finally, the director believes there is only a 50:50 shot that the budget for new sensors would be approved. What is the probability that false alarms will go down?

25% or less

Less than even, but better than 25%

Better than a tossup, but not certain

Guaranteed