Clarice, Dominique, John, and Marco 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 $\mathrm{n}=2$.
(b) What is the probability that Clarice and John attend the conference?
(c) What is the probability that Clarice attends the conference?
(d) What is the probability that John stays home?
(b) The probability that Clarice and John attend the conference is (Round to one decimal place as needed.)
Answer
Final Answer: The probability that Clarice and John attend the conference is \(\boxed{0.167}\).
Step 1 ：The sample space of the experiment is all possible combinations of 2 employees out of 4. This can be calculated using the combinations formula in combinatorics, which is \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, and k is the number of items to choose. In this case, n=4 (total number of employees) and k=2 (number of employees to be chosen for the conference).
Step 2 ：The total number of combinations is 6.
Step 3 ：The probability that Clarice and John attend the conference is the number of ways Clarice and John can be chosen divided by the total number of combinations. Since Clarice and John is a specific pair, there is only 1 way to choose them.
Step 4 ：So, the probability is 1 divided by the total number of combinations.
Step 5 ：Final Answer: The probability that Clarice and John attend the conference is \(\boxed{0.167}\).
