Exam Review Suggestions
	
•	Know how to use a tree diagram in determining a listing of the outcomes or the number of outcomes.
•	Know how to apply the Fundamental Principle of Counting.
•	Know how to define a suitable sample space for some experiment.
•	Know the basic properties of probabilities along with the addition rule and complement rule and how to apply them.
•	Determine expected value (mean) for a probability model.
•	Construct probability models for a game or experiment.
•	Determine variance and standard deviation for a probability model.
•	Be able to construct a histogram for a probability model.

Sample Problems

1. A computer assigns a PIN at random that consists of 4 different digits (repetition is not allowed):    0,1, 2, …, 9.

a. What is the probability that a PIN will have no 0 digit?

b. What is the probability that a PIN will contain only odd digits?

2. A random experiment consists of flipping a fair coin twice and recording the sequence of heads or tails     that occurs.
a. List all the outcomes in the sample space for this experiment.

b. Find the probability of the following events.
	- the coin does not come up heads on either flip

	- the coin comes up heads on both flips.

	- the coin comes up heads exactly once.

	- the coin comes up heads three times.

3. A probability student has found that the teacher always grades quizzes in red, green, orange or purple ink. The probability that the teacher will use red ink is found to be .4. The probability that the teacher will use green is found to be .3, and the probability that the teacher will use orange is .1.

a. What is the probability that the teacher will use either red or orange ink?

b. What is the probability that the teacher will use purple ink?

4. A standard deck of cards contains 52 cards, 13 from each of the four suits: clubs, diamonds, hearts, spades. A gambling game consists of drawing one card at random from a standard deck. You can win 5 dollars if the card is a heart. Otherwise you pay 4 dollars.
A probability model is based on the outcome of a bet.

a. Find the mean of this model.

b. Find the standard deviation of the model.

c. How much money would you expect to win or lose if you play this game once a week for the next year?