Question 2 (15 marks) Your research group grows fruits and grades each one as either good or bad for taste, good or bad for its appearance, and good or bad for its size. As the person in charge of quality of the fruits, your task is to do an analysis to improve the research study. a) Develop your own probability for grade of fruits given in Table Q2. Table Q2 Grade of Fruits Probability Fruits that have good taste Fruits that have both good taste and good appearance Fruits that have good taste and good size, but bad appearance Fruits that have either good size or good appearance (4 marks) Each of the assigned probability must follow these criteria: i. The probability that the fruits have good taste must be greater or equal to 0.70, but smaller or equal to 0.80. ii. The probability that the fruits have both good taste and good appearance must be at least 0.30 and at most 0.45. iii. The probability that the fruits have good taste, good size, but bad appearance must be smaller or equal to 0.025. iv. The probability that the fruits have either good size or good appearance must be greater or equal to 0.48 and smaller or equal to 0.50. V. Each of the probability must be greater than zero. Please denote the events. (2 marks) b) Hence, what is the probability that the fruits have good appearance given the fruits have good taste? (2 marks) c) If the fruits have bad appearance and bad size, what is the probability that the fruits have good taste? (4 marks) d) In order to monitor the progress of your research study, what can you conclude from your answer in (c)? Discuss the result