Math 131

Finite Math

Sample Midterm on Set Theory and Probability

Dr. Wilson

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

a)     AB?       b) AB?

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.

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

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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.

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.

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.

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