Here is a game that’s great for playing while camping. All you need is a 6-sided die and some kind of counting token, say peanuts. This is how you play:

1. You go around the group, taking turns rolling the die.

2. Before each roll, all players “ante up” and put one peanut into the center “pot.” (You do not only ante up on your turn. Rather, everyone must ante up on everyone’s turn.)

3. When it’s your turn, you roll the die once.

4. If the die lands with a 1 or 2 facing up, you must put one more peanut into the pot.

5. If the die lands with a 3 or 4 facing up, you don’t get any peanuts from the pot.

6. If the die lands with a 5 facing up, you take half of the peanuts from the pot. (In the case of an odd number of peanuts, round up. For example, if there are 7 peanuts in the pot, you take 4.)

7. If the die lands with a 6 facing up, you take all of the peanuts from the pot.

To summarize, one turn of the game goes as follows: everyone antes up, the die is rolled, and the player rolling the die acts according to the number on the die. We are at the beginning of your turn (before everyone ants up), and there are 25 peanuts in the pot. There are 7 of you playing.

a) Write down two probability distributions: the distribution of your earnings at the end of your turn, and of the number of peanuts in the pot at the end of your turn

b) Compute the standard deviation of your earnings. Make sure to use the appropriate symbols and show all work If you have 4 peanuts at the beginning of your turn, how many peanuts do you expect to have by the end of your turn?

(d) What’s the probability that there will be less than 20 peanuts left in the pot after your turn?