What are theoritical probabilities?

Answer 1

The word is theoretical, not theoritical nor theoretrical.

There are two main ways of determining the probability of an event. One is the theoretical method in which you have a model of the experiment. You may need to make some assumptions about the model and then you should be able to calculate the relevant probabilities.

Consider, for example, rolling a normal die. There are six possible outcomes: the numbers 1 to 6. You assume that the die is fair (not loaded). [You implicitly also assume that the laws of physics do not change, that the die does not end up on a corner or an edge.] You can then infer that each of the faces has an equal probability of turning up. That is, each has a theoretical probability of 1/6.

You could get a similar result by using the other method for determining probability: the empirical method. Roll the die many times and record the outcomes. Then divide the number of times that 1 turned up by the total number of throws. That is the empirical probability of getting a 1. Similarly for the other numbers. You will find that, if the die is fair and is rolled often enough, these probabilities will be very close to 1/6 even though they might not be exactly that.

So why not simply use theoretical probabilities? There are many times when theoretical probabilities are impossible to calculate because there is insufficient information to build a reliable model. What is the probability that the next car that passes my front door is red? I have no idea how many red cars there are and how many cars in total. Also, do I want all cars in the country or only those within a 20 km radius? If the person next door has a red car but always goes in the direction away from me, she will never be a red car across my door - so distance alone is not good enough. So actually I need to know about cars that have some reason to go past my door. The more I think about it the more complex the model becomes. It is much easier to find a comfy chair and sit and record the colours of cars as they go past. After a while I will have a pretty good idea what proportion of them are red - and that is the empirical or non-theoretical probability.