Clarice, Roberto, Dominique, John, and Marco work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names randomly drawn from a hat. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size \( n=2 \). (b) What is the probability that Dominique and John attend the conference? (c) What is the probability that Clarice attends the conference? (d) What is the probability that Roberto stays home? A. CR,CD,CJ,CM,RD,RJ,RM,DJ,DM,JM,RC,DC,JC,MC,DR,JR,MR,JD,MD,MJ (a) Choose the correct answer below. Note that each person is represented by the first letter in their name. B. CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM C. CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM, CC, RR, DD, JJ, MM D. CR, CD, CJ, CM

The complete list of pairs that can be formed from Clarice, Roberto, Dominique, John, and Marco is CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM. This means the answer is (B). Now, let’s dive deeper! There are a total of 10 unique combinations, each providing an equal chance to each pair. To figure out various probabilities, remember that the chances can often feel like a fun game of chance—after all, it's all about numbers! When it comes to Dominique and John attending, you just have to look for their pair in the combinations (there's only one: DJ). Since there are 10 combinations in total, the probability of Dominique and John being selected is 1/10 or 10%. Now, for Clarice’s attendance, simply note that she could pair with any of the four other attendees. There are four combinations featuring her: CR, CD, CJ, CM—so that gives us a probability of 4/10, or 40%. Finally, as for Roberto, if he's staying home, we look for pairs that don't include him, which are: CD, CJ, CM, DJ, DM, and JM. That makes it 6 favorable outcomes, leading us to a probability of 6/10, or 60%. Isn’t statistics fun when understood!