Probability is all about counting. We count all of the possible states and the states of interest. The ratio is the probability of our state of interest.

This definition implies:

  • Probabilities are a number between 0 to 1.
  • If the probability of an event ocurring is , the probability of it not ocurring is .
  • When events are independent, the probability of them happening together is equal to the product of each of the independent events.

Two events are independent if the outcome of one has no influence on the outcome of the other. A common mistake is to assume independence when that is not the case.

Sample probability

Running a simulation to detect the probabiliy of something might give wrong results, because the event of interest might happen at a different rate. This is called a sample probability, opposed to the true probability of an event. For simulations, doing a lot more tests usually helps.