Assignment:
I. Probability
A. Introduction
1. What is the outcome space? What are the possible values for Pr(A)?
2. If all outcomes are equally probable, what is Pr(A)?
3. What is the notation for the probability of A and B? A or B? A given B? not A?
2. Unconditional probabilities
1. When are outcomes mutually exclusive?
2. When are outcomes independent? What is the conditional probability of A given B? What is the probability of A and B?
3. If the Pr(A) = 2/3 and Pr(B) = 1/3, what are the odds of A?
3. Conditional probabilities
1. Example: drawing cards from a deck
1. a) What is the probability that the first card drawn from a deck of cards is an ace?
2. b) If the first card is an ace, what is the probability that the second will be an ace?
3. c) What is the probability that both will be aces?
2. What is the formula for Pr(A|B)? for Pr(A & B)?
4. Bayes's Rule
1. How can Pr(A) be calculated from conditional probabilities?
2. How can Bayes's Rule be used to find Pr(A|B) from Pr(B|A)?
3. If B is observed outcomes, how can we update the probability of A given that evidence?
a) If you flip a coin ten times and get ten heads, what do you start to think about Pr(H)?