1. A tetrahedral die has its sides labelled A, B, C and D. What is the probability of getting 3 A's in 6 tosses of the die. [10] 2. You are a manager at a company and you need to decide whether to build a large manufacturing facility, a small manufacturing facility, or no facility at all. With a favorable market, you can expect to make R5 400 000 from the large facility or R3 600 000 from the smaller facility. If the market is unfavorable, however, it is estimated that you would lose R1 800 000 with a large facility, and she would lose only R1 200 000 with the small facility. Because of various expenses involved, you have decided to conduct a pilot study to make sure that the market for your product will be adequate. It is estimated that the pilot study will cost her $300 000. Furthermore, the pilot study can be either favorable or unfavorable. Estimates show that the probability of a favorable market given a favorable pilot study is 0.70. The probability of an unfavorable market given an unfavorable pilot study result is estimated to be 0.80. You feels that there is a 0.75 chance that the pilot study will be favorable. Of course, you could bypass the pilot study and simply make the decision as to whether to build a large plant, small plant, or no facility at all. Without doing any testing in a pilot study, you also estimate that the probability of a favorable market is 0.6. What do you recommend? Compute the EVSI. [20]