Question

There are five Oklahoma State Officials: Governor (G), Lieutenant Governer (L), Secretary of State (S), Attorney General (A), and Treasurer (T). Take all possible samples without replacement of size 3 that can be obtained from the population of five officials. (Note: There are 10 possible samples! Make sure to list out the sample space.) (a) What is the probability that the governor is included in the sample? (b) What is the probability that the governor, attorney general and the treasurer are included in the sample?

Answer 1

Person = {G, L, S, A, T}

Sample space: S = {(G, L, S), (G, L, A), (G, L, T), (G, S, A), (G, S, T), (G, A, T), (L, S, A), (L, S, T), (L, A, T), (S, A, T)}

a) P(G is included) = 6/10 = 3/5 or 0.6

b) P(G, A, T) = 1/10 or 0.1

Please comment if any doubt. Thank you.