Problem
Five state officials are listed to the right. a. List the 10 possible samples (without replacement) of size 3 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling.procedure is used to obtain a sample of three officials, what are the chances that it is the first sample on your list in part (a)? the second sample? the tenth sample? a. List all 10 possible samples (without replacement) of size 3 . Use the letter abbreviation for each official. (Use a comma to separate answers as needed.) b. What is the chance that the first sample in your list is selected? (Type an exact answer.) What is the chance that the second sample in your list is selected? $\square$ (Type an exact answer.) What is the chance that the tenth sample in your list is selected? (Type an exact answer.)
Solution
Step 1 ：The 10 possible samples (without replacement) of size 3 are: \(\boxed{('L', 'S', 'A'), ('L', 'S', 'R'), ('L', 'S', 'P'), ('L', 'A', 'R'), ('L', 'A', 'P'), ('L', 'R', 'P'), ('S', 'A', 'R'), ('S', 'A', 'P'), ('S', 'R', 'P'), ('A', 'R', 'P')}\)
Step 2 ：The chance that the first sample in the list is selected is: \(\boxed{0.1}\)
Step 3 ：The chance that the second sample in the list is selected is: \(\boxed{0.1}\)
Step 4 ：The chance that the tenth sample in the list is selected is: \(\boxed{0.1}\)
