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 2000 students in a high school. Among the 2000 students, 1500 students have a laptop, and 900 students have a tablet. 500 students have a laptop and a tablet. Let L be the event that a randomly selected student has a laptop, and T be the event that a randomly selected student has a tablet.( Show all work. Just the answer, without supporting work, will receive no credit.)
( a) Provide a written description of the complement event of( L OR T).
( b) What is the probability of complement event of( L OR T)?
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 an even number.
( a) What is the probability that the sum of the two rolls is at most 6 given that the first one is an even number? 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).