There is a fire sensor system in a building. In long series of experim

namenerk

namenerk

Answered question

2021-12-11

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 2397 from the past data.
The fire sensor system is activated. Find the probability that there was actually a fire.

Answer & Explanation

vrangett

vrangett

Beginner2021-12-12Added 36 answers

Step 1
Given Information :
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 =2397=0.005
First we will draw a probability contingency table with all the information provided:
Sensor system is activateSensor system is not activateTotalThere is fire0.970.005=0.00490.0050.0049=0.00012397=0.005There is no fire0.01(10.005)=0.009950.9950.00995=0.9850510.005=0.995Total0.014850.985151
Step 2
Now, if The fire sensor system is activated. Find the probability that there was actually a fire
We will use the principle of conditional probability:
Sensor system is activatedThere is fire0.970.005=0.0049There is no fire0.01(10.005)=0.00995Total0.01485
P(There is firesensor system is activated)=
P(There is firesensor system is activated)P(sensor system is activated)
P(There is firesensor system is activated)=0.00490.01485=0.329
probability that there was actually a fire =0.329

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