MATH 411, TEST 1
Show all steps for credit. 10 pts. per question
Q1. In how many ways can 8 people be seated in a line of 8 chairs? What
is the probability that Mr. Jones is seated next to Ms. Smith? What is the
probability that there are at least two people between them?
Q2. Urn #1 contains 5 black balls and 4 red balls. Urn #2 contains 4 black
balls and 6 red balls. An urn is picked at random and two balls are removed
from it. If they are both black, what is the probability that urn #1 was
selected?
Q3. A die is rolled once, the number is recorded, and a coin is tossed that
number of times. What is the probability of getting exactly 4 heads?
Q4. The letters in the word ADDRESSES are rearranged randomly. What
is the probability that it still reads ADDRESSES?
Q5. The names of 8 students are listed randomly. What is the probability
that Alice, Jim and Mary are all in the top 4?
Q6. Al, Bill and Charlie can hit a target with respective probabilities 1/2,
2/3, and 3/4. One of them shoots and misses. What is the probability that
it was Al?
Q7. Al and Bob roll a die alternately, the winner being the first to roll a 6.
Al goes first. What is his probability of winning?
Q8. In a hand of 5 cards drawn from 52, what is the probability of having
exactly 2 spades?
What is the probability of having exactly 2 spades and exactly 2 hearts?
What is the probability of having at least one 2 card suit?
Q9. A professor announces to his class that the final will be 10 TRUE/FALSE
questions, and that 7 will be TRUE. Jack does not like to study, so has
decided to randomly choose 3 to answer FALSE, and to answer TRUE to the
remaining 7. What is the probability that Jack will score at least the 80%
that he needs to pass the course? (Since Jack is answering randomly, you
may assume that the correct answers for the first 7 questions are TRUE).
Q10. A die is rolled once and the random variable X is defined to be the
number obtained. Find the mean and variance of X.