STAT 200 Final Examination STAT 200 | Page 4

5. ​ Consider selecting one card at a time from a 52-card deck. What is the probability that the first card is an ace and the second card is also an ace? (Note: There are 4 aces in a deck of cards) (​ Show all work. Just the answer, without supporting work, will receive no credit.) (a) Assuming the card selection is with replacement. (b) Assuming the card selection is without replacement 6. ​ There are 1000 juniors in a college. Among the 1000 juniors, 300 students are taking STAT200, and 150 students are taking PSYC300. There are 50 students taking both courses. Let S be the event that a randomly selected student takes STAT200, and P be the event that a randomly selected student takes PSYC300. (​ Show all work. Just the answer, without supporting work, will receive no credit.) (a) Provide a written description of the complement event of (S OR P). (b) What is the probability of complement event of (S OR P)? 7. ​ Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at most 6, and B be the event that the first one is a multiple of 3. (a) What is the probability that the sum of the two rolls is at most 6 given that the first one is a multiple of 3? ​ Show all work. Just the answer, without supporting work, will receive no credit. (b) Are event A and event B independent? Explain. 8. ​ Answer the following two questions. (​ Show all work. Just the answer, without supporting work, will receive no credit).