QUESTION TWO A. A survey of 200 retail grocery shops revealed the following monthly income pallem: Monthly Income Number of shops Under k20,000 102 K20 000 to k30,000 k30 000 and above 37 (i) What is the probability that a particular shop has a monthly income under k20,0007 [1 Mark] (ii) What is the probability that a selected shop at random has either an income between k20,000 and k30,000 or an income of k30,000 and more? [2 Marks] B. From a computer tally based on employer records, the personnel manager of a large manufacturing firm finds that 15% of the firm's employees are supervisors and 25%% of the firm's employees are college graduates. He also discovers that 5% are both supervisors and college graduates. Suppose an employee is selected at random from the personnel records, what is a probability of (i) selecting a person who is both a college graduate and supervisor? [1 Mark] (ii) selecting a person who is neither a supervisor nor a college graduate? [3 Marks] C. The probability that a new marketing approach will be successful is 0.8. The probability that the expenditure for developing the approach can be kept within the original budget is 0.50. The probability that both of these will be achieved is 0.30. (i) What is the probability that at least one of the objectives will be achieved? [2 Marks] Page 3 of 4 (ii) For the two events described above, determine whether the events are independent or dependent. [2 Marks] D. A man wants to many a girl having the following qualities: Beautiful-the probability of gelling such a girl is one in twenty; has a well paying job-the probability of gelling this one is one in fifty: respectful-the probability here is one in hundred. Find the probability of him getting married to such a girl when the possession of these three altributes is independent. [2 Marks] E. A manufacturing firm produces pipes in two plants I and Il with daily production of 1,500 and 2000 pipes, respectively. The fraction of defective pipes produced by plants I and II are 0.006 and 0.008, respectively. If a pipe is selected at random from that day's production is found to be defective, what is the probability that it came from plant I or plant II? [7 Marks] END OF ASSIGNMENT