Question

clarice, dominique, roberto, marco, and john 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 clarice attends the conference?
(d) what is the probability that marco stays home?

(a) choose the correct answer below. note that each person is represented by the first letter in their name.
○ a. cd, cr, cm, cj, dr, dm, dj, rm, rj, mj
○ b. cd, cr, cm, cj
○ c. cd, cr, cm, cj, dr, dm, dj, rm, rj, mj, dc, rc, mc, jc, rd, md, jd, mr, jr, jm
○ d. cd, cr, cm, cj, dr, dm, dj, rm, rj, mj, cc, dd, rr, mm, jj

Explanation:

Step1: Calculate the number of combinations

The formula for combinations is \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 5\) (total number of employees: Clarice, Dominique, Roberto, Marco, John) and \(k=2\).

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We list the combinations:

• If we use the first - letter notation: \(C\) (Clarice), \(D\) (Dominique), \(R\) (Roberto), \(M\) (Marco), \(J\) (John)
• The combinations are \(\{CD,CR,CM,CJ,DR,DM,DJ,RM,RJ,MJ\}\)

Answer:

A. CD, CR, CM, CJ, DR, DM, DJ, RM, RJ, MJ