A student S is suspected of cheating on exam, due to evidence E of cheating being present. Suppose that in the case of a cheating student, evidence E is present with 60% percent probability, and in the case of a student that does not cheat, evidence E is present with a 0.01 percent probability. Suppose also that the proportion of students that cheat is 1 percent. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided. Required:
a. Determine the events, given probabilities and inferred probabilities.
b. Determine the probability that the evidence is present.
c. Determine the probability that S cheated given the evidence is present.