Please answer the following question with steps, thank you

Your friend has 6 bottles of wine. It is known that precisely one bottle has gone bad (tastes terrible). From inspection of the bottles it is determined that the probability p; that the ith bottle is bad, is given by (p1, p2, ..., P6) = (8/23, 6/23, 4/23, 2/23, 2/23, 1/23). Tasting will determine the bad wine. Your friend ask your help to find the bad wine. Suppose you taste the wines one at a time. Choose the order of tasting to minimize the expected number of tastings required to determine the bad bottle. Remember, if the first 5 wines pass the test you do not have to taste the last. 1. What is the expected number of tastings required? [3 Marks] II. Which bottle should be tasted first? Explain. [2 Marks] Now you get smart. For the first sample, you mix some of the wines in a fresh glass and sample the mixture. You proceed, mixing and tasting, stopping when the bad bottle has been determined. III. What is the minimum expected number of tastings required to determine the bad wine? [3 Marks] IV. What mixture should be tasted first? Explain. [2 Marks]