Question

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?

a 25% or less

b less than even, better than 25%

c better than a tossup, but not certain

d guaranteed

Answer 1

Probability false alarms will go down= Probability it will go down after new system installed + Probability it will go down without new system installation.

Here it is assumed that the director will surely install the new sensors if budget is approved.

"D" be probability false alarm goes down.

"DwN" be probability it goes down with new system.

"DwoN" It goes down without new system.

DwN=1/3(since odds director believes is 1 to 2)

DwoN=1/4(odss not reduced is 3:1 so reverse of that)

Since new sensor depends upon budget approval.

P(New Sensor)=1/2=P(No new sensor)=0.5

Required probability=P(New Sensor)DwN+ P( No new sensor)DwoN

=0.5(1/3)+0.5(1/4)= 0.2917

So answer is b) less than even better than 25%.

Hope you understand.Happy learning.