Elderly population use a smart watch that detects a fall event and sends an emergency message to the police and the EMS. If a person falls the probability of the smart watch categorizing the event as a fall is 0.95. The device does generate false alarms. In last two years there were five incidences where the police arrived on the scene and found out that it was a false event. Police records show that the chances of an elderly person falling on any given day in the community is 2 in 10,000.
If a police receives an emergency message tomorrow, what is the probability that it is a true fall event.

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01-11-2022
Mathematics

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Elderly population use a smart watch that detects a fall event and sends an emergency message to the police and the EMS. If a person falls the probability of the smart watch categorizing the event as a fall is 0.95. The device does generate false alarms. In last two years there were five incidences where the police arrived on the scene and found out that it was a false event. Police records show that the chances of an elderly person falling on any given day in the community is 2 in 10,000.
If a police receives an emergency message tomorrow, what is the probability that it is a true fall event.

Sagot :

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