Clarice comma Marco comma and Roberto 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 equals 2. (b) What is the probability that Clarice and Marco attend the conference? (c) What is the probability that Marco attends the conference? (d) What is the probability that Roberto stays home?

a) S = (CR, MR and MC) = 3

b) 1/3

c) 2/3

d) 1/3

Step-by-step explanation:

a) Let Clarice be 'C', Marco be 'M' and Roberto be 'R'

Since two employees will be selected at random, the sample space will be S = (CR, MR and MC) i. e 3C2 by rule of combination.

b) For probability that Maurice and Clarice attend the conference.

Probability = number of required outcome/total outcome

Required outcome = 1 since MC occurs once in the sample space.

Total outcome = 3 (total number of sample space).

Probability that Maurice and Clarice attend the conference = 1/3

c) Probability that Marco attends the conference will be 2/3 since Marco occur twice in the sample space.

d) Probability that Roberto stays home will be 1/3 since Roberto occurs twice in the sample space i. e (1-2/3)