You may want to read the Wikipedia article on Probability or some Khan Academy video mini-lectures on probability.

#### Basics to Remember

1. Probability is the likelihood that an outcome will happen (e.g., we will roll a 2 on a die).
2. The value of a probability can range from 0 (the event will certainly not happen) to 1 (the even will certainly happen).
3. An "exhaustive" listing of outcomes refers includes everything that could happen.
4. An event is a set of outcomes (e.g., we roll an odd number - outcomes roll a 1, roll a 3, roll a 5).
5. Two events are "mutually exclusive" if the occurrence of one precludes the other. Another way to say this is that they have no outcomes in common.
• Rolling an odd number and rolling an even number are mutually exclusive events. Rolling an odd number and rolling a number less than 3 are not.
6. If the probability of an event A is P(A) then the probability of A not happening is $1 - P(A)$
7. We say that two events are independent if the occurrence of one does not affect the probability of the other.
8. If two events, A and B, are independent, then the probability that A AND B happen is
• $P (A \hspace{2 mm}and \hspace{2 mm}B) = P(A) \times P(B)$
9. IF two events, A and B, are mutually exclusive, then the probability that A OR B happens is
• $P (A \hspace{2 mm}or \hspace{2 mm}B) = P(A) + P(B)$
10. IF two events, A and B, are NOT mutually exclusive, then the probability that A OR B happens is
• $P(A) + P(B) - P (A \hspace{2 mm}and \hspace{2 mm}B)$
11. The conditional probability of A on B is the probability of event A, given the occurrence of event B. This is one of the most important concepts in the social and policy sciences. Conditional probability is written $\mathrm{P}(A \mid B)$, and is read "the probability of A, given B." The value is given by
• $P(A|B) = \frac {P (A \hspace{2 mm}and \hspace{2 mm}B)} {P(B)}$

#### Review Questions Probability

You will need to be able to do these to complete this course successfully.

1. What is the probability of throwing a 1 in a single toss of a single die?
2. What is the probability of throwing a 2 in a single toss of a single die?
3. What is the probability of the event of throwing something less than 3 (that is, 1 OR 2) in a single toss of a single die?
4. What is the probability of the event of throwing two 1s in toss of two dies?
5. What is the probability of the event of throwing something less than 4 (that is, 1 OR 2 or 3) in a single toss of a single die?
6. What is the probability that you threw a 1 given that you threw an odd number in a single roll of a single die?
7. What is the probability that you roll a total of 7 given that your first roll was a 3 when rolling two dice in sequence?
8. What is the probability of the event of throwing something less than 4 (1,2,3) or something odd (1,3,5) in a single toss of a single die?