Suppose that it is known that in an entrance exam, 10% cheat on the exam, and 90% do not. About 70% of the cheaters get a perfect score, while 20% of the noncheaters get a perfect score.
1) What is the probability that a randomly selected student taking the exam will get a perfect score?
2) Give that a student has a perfect score on the exam, what is the conditional probability that it was obtained by cheating?