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 .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.

(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.