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 rule**s

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.