Assignment 3/ 1. A company sets up a committee of employees to monitor health and safety at work. The committee consist of 7 males and 5 females. Two members of the committee are selected at random to be chairperson and secretary. Find the probability that: (a) both the chairperson and secretary are male. (2 m) (b) the chairperson is male and the secretary female. (2 m) (c) chairperson and secretary are from difference gender. (3 m) (CLO2:PLO4:C3) (CLO2:PLO7:C3) 2. An insurance company has calculated that the percentage of its customers who made no claims in previous years was 80%. You may assume that this percentage does not change. If four customers were selected from random, find the probability that, from these four customers: (a) there will be no claims. (2 m) (b) each customer makes a claim. (2 m) (c) there will be at least one claim. (3 m) ((CLO2:PLO4:C3)CLO2:PLO7:C3) 3. A factory uses three machines to produce washers of a given diameter and thickness. Machine A produces 40% of the total production, Machine B 25% of the total production and Machine C 35% of the total production. It is found that 5% of the washers produced by machine A are defective, 4% of those produced by the machine B are defective and 3% of those produced by the machine C are defective. (a) Find the probability that a randomly selected washer is defective. (3 m) (b) Given that a randomly selected washer is defective, find the probability that it was not produced by machine C. (4 m) (c) Given that a randomly selected washer is not defective find the probability that it was produced by machine A or B. (4 m) (CLO2: PLO4:C3) (CLO2:PLO7:C3)4. Psychologists tend to believe that there is a relationship between aggressiveness and order of birth. To test this belief, a psychologist chose 500 elementary school students at random and administered each a test designed to measure the student's aggressiveness. Each student was classified according to one of four categories. The percentages of students falling into the four categones are shown here. Firstborn Not Firstbom Aggressive 20.5% 15% Not Aggressive 10% 54.5% (a) If one student is chosen at random from the 500, is that very high chance to select an aggressive student? Explain. (3 m) (b) Determine the probability that the student is not aggressive, given that the student has either elder brother sister. (3 m) (c) Are the events the student chosen is aggressive and the student is firstbom independent? Prove your answer. (3 m) (CLO2:PLO4:C4)(CLO2:PL07:C4) 5. A woman purchases apartment dweller's insurance at RM130 per year, her furnishings are insured up to maximum of RM10,000. The insurance company from past experience feels that the probabilities of claims of RM500, RM1,000, RM5,000, RM10,000 are respectively 0.1, 0.02, 0.01, 0.001. (a) Determine the expected claim by this woman. m) (b) It is rational for this insurance company to sell this policy? Justify your answer. m) (c) Because the insurance company is losing money from this policy, a company officer asks the premium manager to determine the annual premium required for the insurance companyText Tools 5. A woman purchases apartment dweller's insurance at RM130 per year, her fumishings are insured up to maximum of RM10,000. The insurance company from past experience feels that 0.01, 0.001. the probabilities of claims of RM500, RM1,000, RM5,000, RM10,000 are respectively 0.1, 0.02, (a) Determine the expected claim by this woman. m) (b) It is rational for this insurance company to sell this policy? Justify your answer. m) (2 (c) Because the insurance company is losing money from this policy, a company officer asks the premium manager to determine the annual premium required for the insurance company to make RM50 profit from this policy. Determine the annual premium. (2 m) (CLO2:PLO5:C4) 6. Beyond Beauty Corporation is planning to market a new makeup product. It will earn an annual profit of $5.5 million if this product has high sales and an annual profit of $2.5 million if the sales are medium, and it will lose $3.5 million a year if the sales are low. The probabilities of these three scenarios are 0.40, 0.25 and 0.35 respectively Determine the mean and standard deviation of the annual profit. (9 m) (CLO2 PLO4: C4) (CLO2:PLO7: C4) TOO