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 .
(b) What is the probability that Dominique and John attend the conference?
© What is the probability that Clarice attends the conference?
(d) What is the probability that Roberto stays home?
(a) Choose the correct answer below. Note that each person is represented by the first letter in their name.
A. CR,CD,CJ,CM,RD,RJ,RM,DJ,DM,JM,RC,DC,JC,MC,DR,JR,MR,JD,MD,MJ
CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM
CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM, CC, RR, DD, JJ, MM
(b) The probability that Dominique and John attend the conference is
(Round to three decimal places as needed.)

Question

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

.
(b) What is the probability that Dominique and John attend the conference?
© What is the probability that Clarice attends the conference?
(d) What is the probability that Roberto stays home?
(a) Choose the correct answer below. Note that each person is represented by the first letter in their name.
A. CR,CD,CJ,CM,RD,RJ,RM,DJ,DM,JM,RC,DC,JC,MC,DR,JR,MR,JD,MD,MJ
CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM
CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM, CC, RR, DD, JJ, MM
(b) The probability that Dominique and John attend the conference is
(Round to three decimal places as needed.)

UpStudy AI · Accepted Answer

**(a) Determine the sample space:**  
There are 5 employees (Clarice, Roberto, Dominique, John, Marco) and we want to choose 2 out of 5. The total number of outcomes is  
$$
\binom{5}{2}=\frac{5\times4}{2}=10.
$$  
Listing the pairs (each person represented by the first letter of their name) we have:  
$$
\{CR,\,CD,\,CJ,\,CM,\,RD,\,RJ,\,RM,\,DJ,\,DM,\,JM\}.
$$  
Thus, the correct answer for (a) is the choice:  
**CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM.**

---

**(b) Probability that Dominique and John attend the conference:**  
There is only one favorable outcome $$(DJ)$$ among the 10 equally likely outcomes. Therefore,  
$$
P(\text{Dominique and John attend})=\frac{1}{10}=0.100.
$$

---

**(c) Probability that Clarice attends the conference:**  
Clarice appears in the following pairs:  
$$
\{CR,\,CD,\,CJ,\,CM\}.
$$  
There are 4 favorable outcomes. Thus,  
$$
P(\text{Clarice attends})=\frac{4}{10}=0.400.
$$

---

**(d) Probability that Roberto stays home:**  
Roberto is chosen if his name appears in the pair. The pairs including Roberto are:  
$$
\{CR,\,RD,\,RJ,\,RM\}.
$$  
There are 4 outcomes where Roberto attends, so there are  
$$
10-4=6
$$  
outcomes where Roberto stays home. Thus,  
$$
P(\text{Roberto stays home})=\frac{6}{10}=0.600.
$$
**(a) Sample Space:** CR, CD, CJ, CM, RD, RJ, RM, DJ, DM, JM **(b) Probability that Dominique and John attend:** 0.100 **(c) Probability that Clarice attends:** 0.400 **(d) Probability that Roberto stays home:** 0.600

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