What are the odds?

Probability: the proportion of random trials that result in a desired event occurs over a number of random trials

Mutually exclusive event: Two events that cannot happen simultaneously

Probability distributions

Discrete probability distributions can be produced for discrete numerical events.

Continuous probability densities can be produced for continuous variables.

Addition rules

If two events A and B are mutually exclusive

The probability of an event not occurring

If two events A and B are NOT mutually exclusive we use the general addition rule

Multiplication rules

If two events A and B are independent

You can use tree diagrams to map out complex strings of probabilistic events.

Tree from Openstax.org

Conditional probability and Bayes’ theorem

Conditional probability is the probability that an event occurs given that another event occurs

We can calculate the overall probability of an event by invoking the law of total probability

We can go further and determine the probability of two events happening, even if they are dependent by using the general multiplication rule

Bayes’ theorem is a special use of conditional probabilities.