Finite Math
Sample Midterm on Set Theory and Probability
Skip to 6
1. Let A = {a, b, c, d, e}, and let B =
{a, e, i, o, u}. What is
a)

A


B?

b)

A


B?

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 is 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?
top
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?
top