Q3 (20 points) The medical records of the 445 male diabetics patients reporting to a clinic during one year provide the following results: Diabetes in Parents Age of the Patient I Yes I No Below 20 l 50 l 48 20 to 40 | 72 | 30 Above 40 103 92 Find the probability that: (a) The age of the patients is above 40 and their parents are not diabetics. (b) The age of the patients is above 40 or their parents are not diabetics. (c) The age of the patients is above 40 given that their parents are not diabetics. (d) The age of the patients is between 20 and 40 or their parents are diabetics. If A="The age of the patient is below 20" and B="Patient's parents are diabetics" (e) Are events A and B independent? Justify tour answer. (f ) Are events A and B mutually exclusive? Justify tour answer.Q4 (15 points) According to the Mendelian theory of inherited characteristics, a cross fertilization of related species of red- and white- flowered plants produces a generation whose offspring contain 25% red-flowered plants. Suppose that a horticulturist wishes to cross 7 pairs of the cross-fertilized species. Of the resulting 5 offspring, what is the probability that (a) Let X = the number of red- flowered plants. What is the probability distribution of X? (b) There will be no red-flowered plant. (c) There will be 4 or more red- flowered plants. (d) Find the expected value, variance and the standard deviation of X