### Probability Self-Quiz

A study of forecasting events requires working with probabilities.
For SI679, I will assume you have some familiarity with the concept of
probability and basic discrete probabilities; we will cover additional
required material in the course.
Here, I've included some questions to give you a sense of some of the
concepts and the level I will be assuming at the start of the course.
You should have no difficulty in answering these questions.
#### Sample Questions

Consider rolling a fair 6-sided die, and looking at the side that comes up on
top. The set of possible outcomes is {1,2,3,4,5,6}; because the die is fair, each outcome is equally likely.
Define the following events:

Event A: Number on top is even.

Event B: Number on top is a multiple of 3.

Event C: Number on top is greater than 3.

Let P(x) denote the probability of x.

Q1: What is P(A)? P(A or B)? P(A and B)?

*Answer: P(A) = 1/2; P(A or B) = 2/3; P(A and B) = 1/6.*

Q2: Are events A and B independent?

*Answer: Yes, because P(A and B) = P(A) P(B)*

Q3:What is the conditional probability of C given that A has occured (denoted P(C/A))?

*Answer: P(C/A)= P(C and A)/ P(A) = 2/3 *

Q4:Let random variable X denote the number on top of the die. What is the expectation of X?

*Answer: The expectation is ((1/6)(1 + 2 + 3 + 4 + 5 + 6)) = 3.5.*

#### A final note

I'd be happy to point you to sources to learn/brush up on probabilities.
This is a very useful tool to have at your command, in many areas beyond
the course.