Official Solution: A coffee shop is running a customer raffle in which each slip in a raffle box is labeled either Coffee or Sandwich but not both, indicating the prize on that slip. For one promotional drawing, one slip is selected at random, returned to the box, and then a second slip is selected at random. What is the probability that one selected slip is labeled Coffee and the other is labeled Sandwich? (1) The probability that the two selected slips have the same label is \(\frac{5}{8}\).
Since the two selected slips must either have the same label or different labels, these two outcomes are complementary.
So the probability that the two selected slips have different labels is:
\(1 - \frac{5}{8} = \frac{3}{8}\)
Sufficient.
(2) The number of Sandwich slips in the box is 3 times the number of Coffee slips.
So the probability of selecting a Coffee slip is \(\frac{1}{4}\), and the probability of selecting a Sandwich slip is \(\frac{3}{4}\).
Since the first slip is returned before the second selection, the probability of selecting one of each label is:
\(\frac{1}{4} * \frac{3}{4} + \frac{3}{4} * \frac{1}{4} = \frac{3}{8}\)
Sufficient.
Answer: D