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

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**(a)**  
Since there are three employees and the company chooses any two without regard to order, the sample space consists of all 2‐element subsets of $$\{C, R, M\}$$. These are:  
$$
\{C, R\},\quad \{C, M\},\quad \{R, M\}
$$  
Written with initials, the correct listing is:  
$$
CR,\; CM,\; RM.
$$  
Thus, the correct answer is option **C**.

**(b)**  
The event that Roberto and Marco attend corresponds to the single outcome $$\{R, M\}$$. Since there are 3 equally likely outcomes in the sample space, the probability is:  
$$
P(\{R, M\})=\frac{1}{3}.
$$

**(c)**  
The event that Roberto attends the conference consists of all outcomes that include $$R$$. From the sample space, the outcomes that include $$R$$ are:  
$$
\{C, R\}\quad \text{and} \quad \{R, M\}.
$$  
There are 2 outcomes out of 3, so the probability is:  
$$
P(R\text{ attends})=\frac{2}{3}.
$$

**(d)**  
The event that Clarice stays home means her name is not drawn. The only outcome without $$C$$ is:  
$$
\{R, M\}.
$$  
Thus, the probability is:  
$$
P(\text{Clarice stays home})=\frac{1}{3}.
$$
**(a)** The possible pairs of employees attending are: - Clarice and Roberto (CR) - Clarice and Marco (CM) - Roberto and Marco (RM) So, the correct answer is **C**. **(b)** The probability that Roberto and Marco attend is $$ \frac{1}{3} $$. **(c)** The probability that Roberto attends the conference is $$ \frac{2}{3} $$. **(d)** The probability that Clarice stays home is $$ \frac{1}{3} $$.

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