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
Discrete probability distributions can be produced for discrete numerical events.
Continuous probability densities can be produced for continuous variables.
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
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.