3. (a) A manufactured product is either produced intact or produced with a fault. The probability of a fault is 0.10. An inspection of 10 products, chosen at random, is performed. If at least two of the ten products are found to have a fault, an alarm is raised. i. Calculate the probability that an alarm is raised during an inspection. (4 marks) ii. Given an alarm is raised, what is the probability that there are exactly two faulty products in the inspected sample? (4 marks) iii. Calculate the probability that in 5 independent inspections (each of 10 products), there is at least one alarm raised. (4 marks)