An airport screens bags for forbidden items, and an alarm is supposed to be triggered when a forbidden item is detected. Suppose that 5% 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 an 8% chance that it triggers the alarm. Consider event F as "bags contain forbidden items", event T as "triggers the alarm". If the alarm triggered, what is the probability the bag contains a forbidden item?

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An airport screens bags for forbidden items, and an alarm is supposed to be triggered when a forbidden item is detected.
  • Suppose that 5% 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 an 8% chance that it triggers the alarm.
  • Consider event F as "bags contain forbidden items", event T as "triggers the alarm".

If the alarm triggered, what is the probability the bag contains a forbidden item?

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