During a festive season, a logistic company is requested to arrange product delivery from one warehouse to another warehouse 3 times per day which are morning, noon and night. Throughout the year, the...

During a festive season, a logistic company is requested to arrange product delivery from one warehouse to another warehouse 3 times per day which are morning, noon and night. Throughout the year, the shop owner has observed the rate of defective items caused by the delivery time if the product is delivered in the morning, noon, night, at 2%, 1%, and 5% respectively. The shop owner chooses to request the products to be delivered in the morning, noon, night, at 40%, 50% and 10% respectively. Among all products arrived at the warehouse, if a randomly selected product is not defective, propose the best delivery time that he should adopt in order to have a less chance of receiving defective components. The shop owner insists to arrange the delivery in the morning. Obtain a new rate of defective items for him to alert the driver to take extra care in delivery if he wants the probability of delivery in the morning given a randomly selected product is not defective is greater than 0.5. [25 marks]