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1. Let *A* = {*a*, *b*, *c*, *d*, *e*}, and let *B* =
{*a*, *e*, *i*, *o*, *u*}. What is

2. How many computer passwords are there that consist of 6 characters which can be either letters or digits if the first character has to be a letter? (There are 26 letters and 10 digits.)

3. For which poker hand are there 13xC(4,2)x12xC(4,2)x44/2! possibilities?

4. a) What is a probabilistic model?

b) How do you use a probabilistic model to compute the probability of an event?

5. A bin contains 5 apples and 7 oranges. 6 pieces of fruit are selected at random.

- a) Construct a probabilistic model for this experiment
- b) What is the probability that the sample contains more apples than oranges?
- c) At least one orange?
- d) What is the expected number of apples?

6. A pair of fair dice are rolled and the sum of the numbers on the top faces is noted.

- a) Write out a probabilistic model for this experiment.
- b) What is the probability that the number is even?
- c) What is the probability that the number is divisible by 5?
- d) What is the probability that the number is divisible by 5 given that it is even?
- e) Are being even and divisible by 5 independent events?

7. An urn contains 4 red balls and 8 white balls. 2 balls are drawn at random. Use a tree diagram to construct a probabilistic model for this experiment. Use the model to answer the following questions.

- a) What is the probability of having at least 1 white ball?
- b) What is the probability that the balls are the same color?
- c) What is the probability that the second ball is white?
- d) What is the probability that the second ball is white given that the balls are the same color?
- e) Are the events in b) and c) independent?
- f) What is the expected number of white balls?

8. An instructor passed out midterm reports after the first test. The report contained a homework grade and a test grade. 30% of the class got unsatisfactory grades on both the homework and the test. 60% got satisfactory grades on the homework, and 50% got satisfactory grades on the test.

- a) What percent of the class got satisfactory grades on both the test and the homework?
- b) What percent of the students who got satisfactory grades on the homework got satisfactory grades on the test?
- c) Are getting satisfactory grades on the test and the homework independent events?

9. Linda took a multiple choice test. Each questionhad 4 possible answers from which to choose.There were 6 questions where she had to guess. Make up a probability distribution for this exeriment.

- a) Make up a probability disrtrbution for this experiment.
- b) Draw the graph
- c) What is the probability that she got them all right?
- d) What is the probabity that she got them all wrong?
- e) What is the probability that she got at least 4 right?
- f) What is the probability that she got at least 4 wrong?
- g) What is the expected of correct guesses?