Answer the following questions, ensuring that you show all of your working and reasoning so that your calculations can be followed and understood. Give your answers to appropriate accuracy. a. Two very large batches of identical components, one from supplier A and the other from supplier B, are mixed together. The batches are of equal size. Three components are selected at random. i. What is the probability that two components are from batch A and one is from batch B? ii. What is the probability that the first two components selected are from A and the third is from B? iii. If at least two components are from A, what is the probability that all are from A? iv. Why does it matter that the batches are very large? v. A third batch of components is added to the mix. These additional components are all from supplier A, effectively doubling the number of components from that supplier. Three components are again selected at random. What now is the probability that the two components are from batch A and one is from batch B?