You roll a die. If it comes up a 1 or 2, you win $200. If not, you get to roll again. If you get a 1 or 2 the second time, you win $100. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win.

On the first roll, you have a 1/3 probability of rolling a 1 or 2 and thus winning $200.

There's a 2/3 probability of not rolling a 1 or 2 on the first roll. On the second roll, there is again a 1/3 probability of rolling a 1 or 2, and 2/3 probability otherwise, so that there is a 1/3*2/3 = 2/9 probability of getting a 1 or 2 and thus winning $100, and 2/3*2/3 = 4/9 probability of losing.

(a) Let be a random variable representing the winnings from playing the game. It has the probability mass function

(b) Compute the expected value of :

linear pair postulates