### 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.