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!)
(a) What is the probability that the governor is included in the sample?
(b) What is the probability that the governor and the attorney general are included in the sample?

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Omm2 Omm2 · Answer 1 · 2022-02-02T07:29:45+01:00

So, the required probabilities are,

Part(a):P(A)=0.6

Part(b):P(B)=0.1

Given that:

There are five Oklahoma state officials,

Governor (G), Lieutenant Governor (L), Secretary of State (S), Attorney General (A), and Treasurer (T).

All possible samples of size 3 are obtained from the population of five officials.

Here order does not matter so we use the combinations.

[tex]5_C_3=10[/tex] possible samples.

So, S={GLS,GLA,GLT,GSA,GST,GAT,LSA,LST,LAT,SAT}

Hence, n(s)=10

Part(a):

Let A denotes the event that the governor is included in the sample.

A={GLS,GLA,GLT,GSA,GST,GAT}

That is n(A)=6

So, the probability that the governor is included in the sample,

[tex]P(A)=\frac{n(A)}{n(S)} \\=\frac{6}{10}\\ =0.6[/tex]

Part(b):

Let B denotes the event that the government attorney general and the treasure are included in the sample.

B={GAT}

That is n(B)=1

Hence, the probability that the government attorney general and the treasure are included in the sample is,

[tex]P(B)=\frac{n(B)}{n(S)} \\=\frac{1}{10} \\=0.1[/tex]

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