Probability (Part 2)

• Solutions for Homework #1 are on Blackboard
• Solutions for Homework #2 will be on Blackboard soon
• Reading Assignment for Friday: Chapter 6!! (NO QUIZ)

…or not ¯\(ツ)/¯

https://xkcd.com/1985/

https://www.nytimes.com/interactive/2019/08/29/opinion/hurricane-dorian-forecast-map.html

Definition: The probability of an event not occurring is one minus the probability that it occurs. \[ \mathrm{Pr[{\it not}\ A]} = 1-\mbox{Pr[A]} \]

Definition: The law of total probability is given by \[ \begin{align*} \mathrm{Pr[A]} & = \sum_{B\ \mathrm{in} \ \mathcal{M}}\mathrm{Pr[A \ and \ B]} \\ & = \sum_{B\ \mathrm{in} \ \mathcal{M}} \mathrm{Pr[B]}\ \mathrm{Pr[A\ | \ B]}, \end{align*} \] where \( \mathcal{M} \) is a set of mutually exclusive events such that \[ \sum_{B\ \mathrm{in} \ \mathcal{M}}\mathrm{Pr[B]} = 1 \]

Definition: A probability distribution is a list of the probabilities of all mutually exclusive outcomes of a random trial.

Compare to:

Definition: A probability distribution (or relative frequency distribution) is a list of the probabilities of all values of a random variable in a sample or population.

Probability densities

1. Write out the probability that you are being asked to find. Is it a conditional probability? AND? OR?
2. Identify probabilities that you are given (again, are these conditionals? ANDs? ORs?)
3. Draw a probability tree (if appropriate)