(12 pts.) Suppose that you have the opportunity to win a cash prize by playing a game of chance during the Statistics Department's Applied Probability Night. It costs $2 to play the game. The game starts with you drawing ve cards from a deck, one at a time, Without replacement. The deck is a standard 52-card deck of French playing cards that consists of 52 unique cards, each identied by a particular suit (hearts, spades, clubs, diamonds) and rank (2 through 1 0, along with an ace, king, queen, and jack). The cards you draw are recorded and returned to the deck. The dealer then draws ten cards from the deck, one at a time, without replacement. If the dealer draws three or more of the cards you selected, then you win a cash prize: $50 for three cards, $100 for four cards, and $1,000 for ve cards. If the dealer draws two or fewer of the cards you selected, you do not win any money and have to pay an additional $2. i. Determine whether it seems protable to play the game; i.e., you may assume that your goal is to win money rather than lose money. Explain your reasoning and reference any necessary numerical support. If using an algebraic approach, clearly dene any notation used. If using a simulation approach, be sure to briey describe the logic used to write the simulation and clearly comment your solution code. ii. Suppose you decide to play ten rounds of the game. What is the probability that in ten rounds, you win money in at least one round? Explain your reasoning