.. [15 pts total] Suppose that the Ohio Division of Liquor Control conducted two lotteries: one for 40 bottles of a rare bourbon, and the other for 30 bottles of a rare Scotch. Participants could enter both lotteries, or only one; each winner won (the opportunity to buy) a single bottle of the associated liquor. If a person won both lotteries, they could buy one of each. 60 people just entered the lottery for the bourbon, 50 people just entered the lottery for the Scotch, and 1,000 people entered both lotteries. The Ohio Division of Liquor Control used a random number generator to select the winners in each lottery independently. Sometimes people win both bottles in these lotteries, and the public is concerned that the random selection was rigged. We are interested in the probability that people won both bottles. For example, if the winners of each lottery have no overlap, then 0 people won both bottles; if there is a single individual in both winner lists, then 1 person won both bottles. Let Y be the number of individuals who won both bottles. Use R to simulate the probability distribution of Y. In particular, report: (a) [10 pts] A barplot of the estimated probabilities for different values of Y. (It is okay if not all possible values are displayed in your barplot.) (b) [2 pt] The estimated probability that two people won both bottles. (0) [3 pt] The estimated probability that two or more people won both bottles. Create simulations to answer the following questions. You should report all R code used to obtain the answers - you can either include code interspersed with your responses to the questions, or include a well-commented script at the end of your homework. Include all figures produced, and make sure these figures have appropriate labels and titles. Use n = 10, 000 simulations for all problems. Use full sentences in your answers