To the right are six of the top officials in a region\'s government. a. List the

Question

To the right are six of the top officials in a region's government. a. List the possible samples without replacement of size 4 that can be obtained from the population of six officials. (There are 15 possible samples.) If a simple random sample without replacement of four officials is taken from the six officials, determine the probability the following officials are in the sample. b. The lieutenant governor, governor, and treasurer c. The lieutenant governor and treasurer d. The lieutenant governor a. List the possible samples without replacement of size 4 that can be obtained from the population of six officials. Choose the correct answer below. O A. LSAC, LSAG, LSAT, LSCG, LSCT, LSGT, LACG, LACT, LAGT, LCGT, SACG, SACT, SAGT, SCGT, ACGT O B. LSAC, LSAG, LSAT, LSCG, LSCT, LSGT, LACG, LACT, LAGT, LCGT, SACG, ASLT, CASL, GASL, TASL O C. LLLL, SSSS, AAAA, CCCC, GGGG, TTTT, LLSS, SSAA, CCGG, GGTT, LLAA, AAGG, GGSS, SSTT, TTCC O D. LLSA, LLCG, SSAC, SSGL, AACG, AATL, CCGT, CCLS, GGLS, GGAC, TTSA, TTCG, LLLL, SSSS, AAAC b. The probability that the lieutenant governor, governor, and treasurer are in the sample is | |. (Type an integer or a simplified fraction.) c. The probability that the lieutenant governor and treasurer are in the sample is | |. (Type an integer or a simplified fraction.) d. The probability that the lieutenant governor is in the sample is | |. (Type an integer or a simplified fraction.) Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Chief of Staff (C) Governor (G) Treasurer (T)

Explanation / Answer

a) Option A

Option B has LSAT and ASLT repeating and hence invalid

Option C has LLLL which is invalid

Option D has LLSA which is invalid

b) P(lieutenant governor, governor and treasurer) = 3/15 = 1/5

c) P(lieutenant governor and treasurer) = 6/15 = 2/5

d) P(lieutenant governor is in the sample) = 10/15 = 2/3

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