Statistics

        1. (1 point) Probability is a measure of how likely an event is to occur. Match one of the probabilities that follow with each statement of likelihood given. Type the correct letter in each box. You must get all of the answers correct to receive full credit. 1. This event is very unlikely to happen, but it will occur once in a while in a long sequence of trials. 2. This event will occur more often than not. 3. This event will occur a little less than half the time over a long sequence of trials. 4. This event is very likely to occur. A. 0.02 B. 0.44 C. 0.92 D. 0.58 2. (1 point) Government data assign a single cause for each death that occurs in the United States. In a certain city, the data show that the probability is 0.3 that a randomly chosen death was due to cardiovascular (mainly heart) disease, and 0.25 that it was due to cancer. (a) The probability that a death was due either to cardiovascular disease or to cancer is . (b) The probability that the death was due to some other cause is . 3. (1 point) For each problem, select the best response. (a) A phenomenon is observed many, many times under identical conditions. The proportion of times a particular event occurs is recorded. This proportion represents • A. the variance of the event. • B. the probability of the event. • C. the correlation of the event. • D. the distribution of the event. (b) The collection of all possible outcomes of a random phenomenon is called • A. the probability. • B. a census. • C. the sample space. • D. the distribution. • E. None of the above. 4. (1 point) Given that P(A) = 0.8 and P(B|A) = 0.31, find the joint probability P(A and B): P(A and B) = 5. (1 point) Approximately 9% of people are left-handed. If two people are selected at random, what is the probability of the following events? A. P(Both are right-handed) = B. P(Both are left-handed) = C. P(One is right-handed and the other is left-handed) = D. P(At least one is right-handed) = 6. (1 point) Four candidates are running for mayor. The four candidates are Adams, Brown, Collins, and Dalton. Employing the subjective approach, a political scientist has assigned the following probabilitites: P(Adams wins) = 0.55 P(Brown wins) = 0.08 P(Collins wins) = 0.25 P(Dalton wins) = 0.12 Determine the probabilities of the following events: Adams loses = Either Brown or Dalton wins = Either Adams, Brown, or Collins wins = 7. (1 point) Suppose that A and B are two events for which P(A) = 0.15, P(B) = 0.7, and P(B|A) = 0.42 Find each of the following: A. P(A and B) = B. P(A or B) = C. P(A|B) = 8. (1 point) If P(A) = 0.20, P(B) = 0.30 and P(A and B) = 0.06, then A and B are: • A. dependent events • B. independent events • C. mutually exclusive events • D. complementary events A useful graphical method of constructing the sample space for an experiment is: • A. a pie chart • B. a tree diagram • C. a histogram • D. an ogive 1 9. (1 point) A department store analyzed its most recent sales and determined the relationship between the way a customer paid for an item and the price category of the item. The joint probabilities are given in the table below. Cash Credit Card Debit Card Under 20 Dollars 0.1 0.02 0.05 20-100 Dollars 0.05 0.21 0.17 Over 100 Dollars 0.02 0.24 0.14 A. What proportion of purchases were paid with a debit card? Proportion = B. Find the probability that a credit card purchase was for over 100 dollars. Probability = C. Determine the proportion of purchases made by credit card or debit card. Proportion = 10. (1 point) In a survey of 153 people, the following data were obtained relating gender to color-blindness: Color-Blind (C) Not Color - Blind C Total Male (M) 72 28 100 Female (F) 35 18 53 Total 107 46 153 A person is randomly selected. What is the probability that the person is: a) Male? b) Male and Color-blind? c) Male given that the person is Color-blind? d) Color-blind given that the person is Male? e) Female given that the person is not Color-blind? f) Are the events Male and Color blind independent? Enter yes or no . 11. (1 point) What is the probability that a 8-digit phone number contains at least one 1? (Repetition of numbers and lead zero are allowed). Answer: 12. (1 point) An experiment consists of choosing a subset from a fixed number of objects where the arrangement/order of the chosen objects is not important. Determine the size of the sample space when you choose the following: (a) 5 objects from 27 Answer : (b) 4 objects from 22 Answer : (c) 7 objects from 9 Answer : Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 2