Question

clance, 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 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 clance and roberto attend the conference?
(c) what is the probability that clance 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.
oa. cr, cj
ob. cr, cj, rj, rc, jc, jr
oc. cr, cj, rj, cc, rr, jj
od. cr, cj, rj

Explanation:

Step1: Find sample - space

We have 3 people (Clance - C, Roberto - R, John - J) and we want to select 2. Using combination concept, the possible pairs are (C,R), (C,J), (R,J). So the sample - space S = {CR, CJ, RJ}.

Step2: Calculate probability for part (b)

The probability formula is $P(E)=\frac{n(E)}{n(S)}$. Here, the event E that Clance and Roberto attend is {CR}. n(E) = 1 and n(S)=3. So $P=\frac{1}{3}$.

Step3: Calculate probability for part (c)

The event that Clance attends means the pairs are {CR, CJ}. n(E) = 2 and n(S)=3. So $P=\frac{2}{3}$.

Step4: Calculate probability for part (d)

The event that Roberto stays home means the pairs are {CJ}. n(E) = 1 and n(S)=3. So $P=\frac{1}{3}$.

Answer:

(a) D. CR, CJ, RJ
(b) $\frac{1}{3}$
(c) $\frac{2}{3}$
(d) $\frac{1}{3}$