List of probability topics:

P(x,y) is the same as P(x \cap y)

A very common notation that you need to understand is that is the same thing as saying .

Learned this to learn about how we can create AI that makes optimal decisions given limited information and uncertainty.

The classical definition of probability:

However, there are 3 problems with this classical definition:

  1. Logically inconsistent
  2. Elements in may be difficult to count
  3. needs to be finite (in the case for example of infinite sample space)

There are two extended interpretations of probability:

4-Part Method

  1. Identify the sample space (i.e. outcomes) helps to use a tree
  2. Define Events of Interest (ex: when you win)
  3. Determine Outcome Probabilities
    • Assign Edge Probabilities
    • compute Outcome Probabilities
  4. Compute Event Probabilities

Variables vs. Events?

Unconditional Probability Unconditional probability is the degree of belief in a proposition in the absence of any other evidence. The result of rolling a die is not dependent on previous events.


It’s easy to create an arbitrary distribution over (0,1). Just take any function that doesn’t blow up anywhere between 0 and 1 and stays positive. Then, simply integrate it from 0 to 1 and divide the function with that result.