MATH 534 Week 2 Quiz

1. Question: If X = {1, 2, 4, 8, 9, 10, 16} and Y = {3, 4, 7, 9, 15}, then X ∩ Y is _________. 2. Question: If the occurrence of one event precludes the occurrence of another other event, then the two events are ______________. 3. Question: A listing of all elementary outcomes (i.e. the outcomes which cannot be broken down into other events) of an experiment (i.e. a decision making situation under uncertainty) is called a _____________. 4. Question: The probability that an event, Event A, occurs is 0.70. The probability of another event, Event B, occurs 0.67. The probability of both A and B occur is 0.50. The probability that either Event A or Event B occurs is _____________. 5. Question: If two events, Event A with probability P(A) and Event B with probability P(B) are mutually exclusive, then ____________. 6. Question: For two events A and B, suppose P(A)=0.6, P(B)=0.2, and P(A|B)=0.7, then P(A U B)= ____________. 7. Question: Fifty percent of all technical assistants would like to have a PC. Eighty percent of all technical assistants would like to have MAC. Forty-five percent of all technical assistants would like to have both. If a technical assistant is randomly selected, what is the probability that she would like to have MAC, given that she would like to have a PC as well? 8. Question: The probability of one event given the information that another related event has occurred is an example of ____________. 9. Question: Consider the following 3 x 4 contingency table in which a sample of 1400 companies is summarized in terms of the company’s industry type (X, Y, or Z) and geographic location (A, B, C, or D). 10. Question: What is the probability P(B│Y)? 11. Question: If two events, Event A with probability P(A) and Event B with probability P(B) are independent, then the conditional probability P(A│B) is ______________. 12. Question: Random variables, which are usually generated from experiments in which the observations or things are “measured” rather than “counted”, are _____________. 13. Question: The random variable, “number of people who arrive at a store during a 15-minute interval,” is an example of __________. 14. Question: The random variable, which describes the “time between customer arrivals at a retail store,” is an example of __________. 15. Question: Consider the following discrete random distribution. 16. Question: What is the variance of the distribution? 17. Question: Thirty percent of the people called agree to participate in a brief telephone survey. In a random sample of four people called, what is the probability that exactly two people would not agree to participate in the survey? 18. Question: What is the variance of a binomial distribution in which the number of trials n = 100 and the probability of success p = 0.5? 19. Question: A dealer in a casino has rolled a 6 on a single die four times in a row. What is the probability of his rolling another 6 on the next roll, assuming it is a fair die? 20. Question: The standard deviation of the number of defectives in samples of 200 units taken periodically from the output of a machine that has a 0.5% defective rate is . One fair coin is tossed 10 times, what is the probability of getting at least 8 heads out of 10 tossing experiments? 21. Question: One fair coin is tossed 25 times, let X be the number of getting heads out of those 25 tossing experiments. What is the mean and variance of X?