Show every step clearly with formula and explain all the logic.?Write clearly

(P1, P2, - ... 8 6 4 2 2 23 23 23 23 23 23 5. One is given 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 pi that the ith bottle is bad is given by ,P6) = 23). Tasting will determine 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 don't have to taste the last. (a) What is the expected number of tastings required? (b) Which bottle should be tasted first? (c) Now you get smart. For the first sample, you mix some of the wines in a fresh glass and sample the mixture. You proceed, mix- ing and tasting, stopping when the bad bottle has been deter- mined. What is the minimum average number of tastings required to determine the bad wine? Explain the tasting method