Suppose you roll a pair of honest 8 sided dice and subtract them: larger - smaller. Use to answer the following questions. A. Write out the sample space with the probability function. (Hint: write out all equally likely outcomes first and use.) B. What are the odds of rolling a difference of 2? C. What is one possible simple event here? D. What is one possible certain event here? E. If you roll a difference of 7, you win $20, if you roll a difference of 2 you win $5. If you roll anything else you loose $2. What is the expected value of the experiment? (Hint: Long term average?)