4) A laptop manufacturer estimates the probability of a mechanical defect within the one-year warranty period is 0.7. The probability of any other defect is 0.4. The probability of encountering both types of defects is 0.15 [3 marks]a) What is the probability of encountering any type of defect? b) What is the probability of not encountering a defect? 5) Determine the probability that when two dice are rolled the sum of the numbers is greater than 7, given that one of the die does not turn up a 4. [2 marks] 6) In a college course, 40% of students do not complete their assigned work. Overall, 25% of students fail the course. Of all the students, 15% do not complete their assigned work and fail the course. Are the events (failing the course; and not completing assigned work; independent? Mathematically justify your reasoning. [2 marks] 7) A bag of candy contains 6 gummy bears, 9 starbursts and 5 skittles. Three candies are drawn from the bag and eaten, one at