Dominique, Marco, Roberto, 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 drawn from a hat. This is like obtaining a simple random sample of size 2. (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 Dominique and Marco attend the conference? (c) What is the probability that John attends the conference?

Answer: (a) S = (RD, RC, RM, RJ, DC, DM, DJ, CM, CJ, MJ)

(b) P (D and M) = 1/10 = 0.1

(c) P (J attends) = 4/10 = 0.4

Step-by-step explanation:

(a) To get the sample space we will use the first letter of each person's name:

D = Dominique; M = Marco; R = Roberto and J = John.

The sample space is a random sample of size 2, that is all possible combinations of persons present;

Sample space, S = (RD, RC, RM, RJ, DC, DM, DJ, CM, CJ, MJ)

(b) Probability that Dominique and Marco will attend the conference is the number of times in which both Dominique and Marco attend together divided by the total number of elements in the sample space.

There is only one instance in which both Dominique and Marco can attend the conference together and there is a total of 10 possible outcomes in the sample space, thus;

P (D and M) = 1/10 = 0.1

(c) Probability that John attends the conference an be found by checking all the outcomes in the sample space where John attends divided by the total number o possibilities in the sample space.

P (J attends) = 4/10 = 0.4