Exercise 2 One of Adam's faVOrite casino games is called \"Craps\". In the rst round of this game, two fair 6-sided dice are rolled. If the sum of the two dice equal 7 or 11, Adam doubles his money! If a 2, 3, or 12 are rolled, Adam loses all the money he bets. a. Based on your lecture notes, what is the chance Adam will double his money in the rst round of the game? What is the chance Adam will lose his money in the rst round of the game? b. Let's now approximate the results in (a) by simulation. First, set the seed to 123. Then, create an object that contains 5,000 sample rst round Craps outcomes (simulate the sum of 2 dice, 5,000 times). Use the appropriate function to visualize the distribution of these outcomes (hint: are the outcomes discrete or continuous?). c. Imagine these sample results happened in real life for Adam. Using R functions of your choice, calculate the percentage of time Adam doubled his money. Calculate the percentage of time Adam lost his money. d. Adam Winning money and Adam losing money can both be considered events. Are these two events independent, disjoint, or both? Explain why. e. Quickly mathematically verify by calculator if those events are independent using part (a) and What you learned in lecture. Show work