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# Five state officials are listed to the right. a. List the 10 possible samples​ $without replacement$ of size 33 that can be obtained from the population of five officials. Lieutenant GovernorLieutenant Governor ​$Upper LL​$ Secretary of StateSecretary of State ​$Upper SS​$ Attorney GeneralAttorney General ​$Upper AA​$ RepresentativeRepresentative ​$Upper RR​$ Press SecretaryPress Secretary ​$Upper PP​$ b. If a simple random sampling procedure is used to obtain a sample of threethree ​officials, what are the chances that it is the first sample on your list in part​ $a$? the second​ sample? the tenth​ sample?

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## Answer to a math question Five state officials are listed to the right. a. List the 10 possible samples​ $without replacement$ of size 33 that can be obtained from the population of five officials. Lieutenant GovernorLieutenant Governor ​$Upper LL​$ Secretary of StateSecretary of State ​$Upper SS​$ Attorney GeneralAttorney General ​$Upper AA​$ RepresentativeRepresentative ​$Upper RR​$ Press SecretaryPress Secretary ​$Upper PP​$ b. If a simple random sampling procedure is used to obtain a sample of threethree ​officials, what are the chances that it is the first sample on your list in part​ $a$? the second​ sample? the tenth​ sample?

Sigrid
4.5
a. To find all possible samples of size 3 that can be obtained from a population of 5 officials, we can use combinations.
There are 5 officials, denoted as LL, SS, AA, RR, PP.
The number of ways to choose a sample of 3 officials without replacement from 5 officials is given by {5 \choose 3} = \frac{5!}{3!$5-3$!} = 10 .

The 10 possible samples are:
1. LL, SS, AA
2. LL, SS, RR
3. LL, SS, PP
4. LL, AA, RR
5. LL, AA, PP
6. LL, RR, PP
7. SS, AA, RR
8. SS, AA, PP
9. SS, RR, PP
10. AA, RR, PP.

b. If a sample of size 3 is chosen at random, each sample of 3 officials has the same probability of being chosen, as each sample is equally likely.
Therefore, since there are 10 total samples, the probability of choosing each sample is \frac{1}{10} .

So, the chances of the sample being the first, second, or tenth sample from the list are all \frac{1}{10} .

\textbf{Answer:} The chances that the sample is the first, second, or tenth sample are all \frac{1}{10} .

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