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).