Question 2 (40%) Consider a hypothetical instant lottery ticket with the following prizes and probabilities: Prizes Probabilities $1,000,000 1 in 1,200,000 $5,000 1 in 5,750 $2,000 1 in 7,500 $1,000 1 in 1,000 $500 1 in 700 $200 1 in 500 $100 1 in 50 Assume that the instant lottery has only one winning chance, and the rest of the probability (1 minus the sum of all probabilities on the list) is to end with no prize. In addition, assume that A French wheel has 37 possible outcomes (number 0 to 36). Assume that the French wheel is fair, and the probability of getting any one of the numbers with a single spin is - "You may keep a and e in your solution.the sales of the lottery are so large that whether one lottery ends with winning a prize can be approximately regarded as independent to others' results. i. What is the expected payoff of this instant lottery? ii. If you have 10 such instant lotteries, what is the probability of having all of them end with no prize? iii. If you have 10 such instant lotteries, what is the probability of having exactly 7 of them end with no prize? iv. Suppose now you know that among those 10 instant lotteries you have, exactly 7 of them end with no prize. What is the probability that by randomly picking 3 instant lotteries from the 10 you have, at least 2 out of the 3 end with no prize