A definition of probabilities

An event is something that can be either true or false

ex. You may win the lottery next year

The probability of that event is a rational evaluation of how much we believe the event is true, given all the information available to us

A typical definition of probabilities

Often we see the definition \[\text{Probability}=\frac{\text{positive cases}}{\text{total cases}}\]

The problem is how do we count positive and total cases?

Example: We have several red and blue cards, and we take one randomly.

What is the probability that the card is blue?

The answer depends on what we know

• If we know all possible outcomes, and they are “symmetric”, then each one of them has the same probability

  • For instance, all the dice sides are “symmetric”, thus they have all the same probabilities

• If the event is true only for a set of outcomes, and the outcomes are “symmetric”