. There is a fire sensor system in a building. In long series of experiments, it was found that the accuracy of the fire sensor system can be described as follows: • In the case of a fire, the sensor system will be activated with probability 0.97. • In a night without fire, the sensor system may be activated with probability 0.01. The probability of a fire in this specific area is founded 2/397 from the past data. The fire sensor system is activated. Find the probability that there was actually a fire.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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5. There is a fire sensor system in a building. In long series of experiments, it was found that the accuracy
of the fire sensor system can be described as follows:

In the case of a fire, the sensor system will be activated with probability 0.97.

In a night without fire, the sensor system may be activated with probability 0.01. The probability
of a fire in this specific area is founded 2/397 from the past data.
The fire sensor system is activated. Find the probability that there was actually a fire.

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