Clarice, Roberto, 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 Roberto and Marco attend the conference? (c) What is the probability that Roberto attends the conference? (d) What is the probability that Clarice stays home? (a) Choose the correct answer below. Note that each person is represented by the first letter in their name. A. CR, CM, RM, RC, MC, MR B. CR, CM, RM, CC, RR, MM C. CR, CM, RM D. CR, CM

The sample space consists of all possible pairs of employees that can be drawn from the group. For this scenario, the unique pairs of team members are: CR (Clarice and Roberto), CM (Clarice and Marco), and RM (Roberto and Marco). So the answer is C. CR, CM, RM. If we want to determine the probability that Roberto and Marco attend the conference, there are 3 possible combinations of pairs (CR, CM, RM). Since only one combination includes both Roberto and Marco, the probability is 1 out of 3, or \(\frac{1}{3}\). The probability that Roberto attends the conference can be calculated by finding how many pairs include him. The pairs are CR, CM, and RM; thus, he is in 2 of the 3 pairs, giving a probability of \(\frac{2}{3}\). To find the probability that Clarice stays home, we see that she only isn’t included in one pair—RM (Roberto and Marco). Therefore, the probability that Clarice stays home is also \(\frac{1}{3}\).