Solved Problems On Bayes Theorem
Bayes’ theorem is a powerful method for addressing the inverse problem in general.In the last section of the post, I’m going to demonstrate how to do this with a toy example.The most common result is that the window will break.If your neighbor later asks if you know anything about the incident, you can confidently inform him that his window was broken you threw a rock at it earlier. But what if it wasn’t you who broke the window and, in fact, you have no idea what broke it? Was there a large temperature difference between the center and the periphery of the glass which caused a spontaneous breakage?This is the initial probability that the light bulb is on. This is the evidence that alters p(i) to a more accurate value.Now, you try to gather evidence that will tell you if the light bulb is on or not. So we finally get p(i/switch) that is the probability of light being on given that the switch is on.This very simple example helps us understand the Bayes rule for an uncomplicated case.This theorem can be extended to many cases which are more complicated.
For example, the union of getting a king or hearts in a deck of cards would include 16 cards (13 hearts and 3 kings).
Or was it a spontaneous breakage caused by a fabric defect?
You see, unlike the previous question, this one is actually not straightforward to answer.
Event – An event is simply the outcome of an experiment.
For example, if you pick out a card and get a queen of spades, it is an event.