7. Make a bet? Your crafty teacher makes every student in the class a simple offer. Your teacher has an octahedron-of-chance (an eight-sided die). Every student rolls once. If you roll an 8, you get five extra credit points on the next test. If you roll anything else you roll again. If on the second roll, you roll a number 3 or higher, you get a two-point bonus on the test, but if not, you lose one point! (This is not legal in most states.) a) make a probability model for the number of points a stu- dent in the class will receive/lose. b) Find the expected number of points the teacher will award to students in this class on average. c) Would you play? Why or why not?