I LAMI I E [TY LLE E I-IANA [SBA 256: BASIC STATISTICS EXERCISE 1 1) If3 out of 24 marked scripts have mathematical errors and 5 are to be randomly selected for audit, what is the probability that none of the marked scripts with mathematical errors will be chosen? 2) Ten identical PCs are in the inventory ofa dealer, and one has a hidden defect. If 3 are to be shipped, and the computers are selected in such a way that each has the same probability of being shipped, find the probability that the computer with the hidden defect will be shipped 3) If the probabilities are 0.87, 0.36 and 0.29 that a family, randomly chosen as part of a sample survey in Adentan, owns a color television set, a video cassette recorder or both, what is the probability that a family in this area will own one, or the other or both kinds of sets? 4) The probability that a woman trying on a dress will ask to have it altered is 0.55, the probability that she will ask to have it delivered to her home is 0.32 and the probability that she will ask to have both done is O.21.What is the probability that a woman shopping in this store will ask a) either to have the dress altered or to have it delivered to her home; b) neither to have it altered nor to have it delivered to her home? 5) Among 90 pieces of mail delivered to the library of IUCG, 50 are addressed to the Faculty of Business Administration and 40 are addressed to the Communication Faculty. If two of these pieces of mail are delivered to the Dean's office by mistake, and the selection is random, what are the probabilities that a) both of them should have been delivered to the Faculty of Business Administration; b) both of them should have been delivered to the Faculty ofArts; c) one should have been delivered to the Faculty of Arts and other to the Faculty of Business Administration?. 6) A manufacturing company operates two machines. The probability that the rst machine breaks down in the next week is 0.14. The probability that the second machine breaks down in the next week is 0.17. The probability that both machines break down in the next week is 0.06. Calculate: a) the probability that the first machine does not break down in the next week. b) the probability that at least one machine breaks down in the next week. c) the probability that exactly one machine breaks down in the next week. 7) The probability that a policyholder will make a claim on his homeowners' insurance policy during the next year is 0.4-4.The probability that a policyholder will make a claim on his automobile insurance policy during the next year is 0.36. The probability that a policyholder will make a claim on both his homeowners' insurance policy and his automobile insurance policy during the next year is 0.21. Calculate the probability that a randomly selected policyholder does not make a claim on either his homeowners' insurance policy or his automobile insurance policy. 8) A recent survey asked 100 people ifthey thought women in Ghana should be permitted to run for the highest office. The results of the survey are shown below. Find these probabilities: a) The respondent answered 'Yes' given that the respondent was a female. b) The respondent was a male, given that the respondent answered 'No'. 9) A poll found that 44% of Ghanaians say they eat TZ every weekend. If three people are selected at random, find the probability that three will say they eat TZ every weekend. 10) The State lnsurance Company found that 43% of residents of Accra had life insurance with its company. Ofthese clients, 20% also had automobile insurance with company. lfa resident of Accra is selected at random, find the probability that the resident has both life and automobile insurance with the state insurance company. 11) Alhassan and Bawa are planning to form a partnership to build and operate a number of "car- wash bases" and that Alhassan feels that there is a fifty-fty chance that any new unit will show a prot for the rst year. Bawa feels that the odds are 2 to 1. Due to Alhassan's experience, he is three times likely to be right as Bawa. Suppose the partnership come into being and out of the six units opened, five ofthem showed a profit for the first year and the sixth showed a loss. Find the probability that a) Alhassan is right. b) Bawa is right