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
(b) the probability that roberto and marco attend the conference is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate total number of samples

The formula for combinations is \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 5\) (number of employees) and \(k=2\) (number of employees to be selected).

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The sample space is as in option A (CD, CR, CM, CJ, DR, DM, DJ, RM, RJ, MJ)

Step2: Probability that Roberto and Marco attend

There is only 1 favorable outcome (RM) out of 10 total outcomes.
The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{10}=0.1\)

Answer:

\(0.1\)