Rebecea Lobo and Kara Lawson have a debate on the Today show with Hoda and Jenna about a new game. The game is as follows: You must pay $100 to play. Then a fair [ ten sided } die is rolled until a 7 appears. If a 7 appears on the k" roll, you win (If)la dollars. The game nishes when a T appears. Let Z be a random variable that represents your winnings from the game. 1. Kara believes that you should play the game since the expected payoff is greater than its cost of $190., however. Rebecca disagrees. Compute the expected payoff and see if Kara or Rebecea is correct. 2. Suppose now that you have to pay $1ElI million dollars to play the game. do you think Kara would play this game? Give a probabilistic reasoning to explain your