namenerk

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$\frac{2}{397}$ from the past data.

The fire sensor system is activated. Find the probability that there was actually a fire.

- 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

The fire sensor system is activated. Find the probability that there was actually a fire.

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

First we will draw a probability contingency table with all the information provided:

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:

probability that there was actually a fire