Question 2. Suppose that, in anticipation of an exam, you roll a six-sided die. You commit to the following plan: if the die rolls 6, you will study hard for the exam, if the die roll is 4 or 5, you will study a little, and if the roll is 1, 2. or 3 you will not study at all. Suppose that by studying hard for the exam, you secure a 95% chance of passing the exam, that by studying a little you have a 70% chance of passing, and that by not studying you have a 10% chance of passing. Now suppose you wake up after the exam with no memory of what happened, to find out that you miraculously passed the exam. What is the probability that you did not study for the exam