# How to calculate the new conditional probability in a baseyan network when an evidence on one attribute is provided?

I'm trying to understand bayesan networks also I created a simple bayesan network according to same sample date.

This is the network (created with Hugin Lite)

There is one class (Failure) and two attributes (light and temperature).

Failures = kinds of failure (three possible values: Mechanic , Electric , None) Light = indicates if a light is on or off when there is a failure (which can be Mechanic OR Electric) Temperature = indicates the temperature (three possible values: low,normal,high)

Light and temperature are independent variables

In the beginning there is NO EVIDENCE about variables. These are the probability tables of "A PRIORI probability":

Now an EVIDENCE is provided. So we'll have a "A POSTERIORI Probability"

We know that:

• Light is ON (so in the first table there will be just one row: Light = ON)
• Temperature is LOW (so in the second tablet there will be just one row: Temperature = LOW)

The column of both table remain the same (Mechanic,Electric,None).

My question is: how should I update conditional table?

I'm sure there is some relationship with "Bayes formula" but I'm a bit confused.

This was an homework but I'll have to a similar (not the same) homework next month for an university project. My aim is to understand how to calculate the new probability.

Thank you in advance for any hint.

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