Question

An airport screens bags for forbidden items, and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that 1% of bags contain forbidden items. If a bag contains a forbidden item, there is a 98% chance that it triggers the alarm, and if a bag doesn't contain a forbidden item, there is a 6% chance that it triggers the alarm. A bag is chosen at random, What is the probability it contains a forbidden item and triggers the alarm?

Answer 1

Solution:

We will use tree diagram to solve this problem.

“Suppose that 1% of bags contain forbidden items”

“If a bag contains a forbidden item, there is a 98% chance that it triggers the alarm.”

“If a bag doesn't contain a forbidden item, there is a 6% chance that it triggers the alarm.”

From the above two facts, let us draw the next branches of the tree diagram.

Since 1% of bags contain forbidden items and 98% of those bags triggers the alarm so the probability that the bag contains a forbidden item and triggers the alarm is calculated by multiplying those probabilities.

Therefore,P(FA)=0.01*0.98=0.0098

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