Question

Oklahoma State Officials. Refer to Table 5.1 on page 196.

(a). List the possible samples without replacement of size 4 that can be obtained from the population of five officials. (Hint: There are five possible samples.)

If a simple random sample without replacement of four officials is taken from the five officials, determine the probability that

(b). the governor, secretary of state, attorney general, and treasurer are obtained.

(c). the governor and treasurer are included in the sample.

(d). the governor is included in the sample.

Short answer

Part (a) GLSA, GLST, GLAT, GSAT, LSAT

Part (b) 0.2

Part (c) 0.6

Part (d) 0.8

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Refer to Table 5.1 on page 196.

Table 5.1 shows the following:

Five Top Oklahoma state officials:

Governor (G)

Lieutenant Governor (L)

Secretary of State (S)

Attorney General (A)

Treasurer (T)

Part (a) Step 2. List the possible samples without replacement of size 4 that can be obtained from the population of five officials.

In each sample, only one official can be chosen at a time.

As a result, the following consequences are possible:

GLSA, GLST, GLAT, GSAT, LSAT

Part (b) Step 1. Determine the probability that the governor, secretary of state, attorney general, and treasurer are obtained if a simple random sample without replacement of four officials is taken.

A simple random sample with no replacement is utilized to choose the four of the five officials.

The number of positive outcomes divided by the total number of possible outcomes is the likelihood.

GSAT is a possible consequence out of a total of 5 possible outcomes.

As a result, a sample of the governor, attorney general, and treasurer has a chance of:

$\frac{1}{5}=0.2$

Part (c) Determine the probability that the governor and treasurer are included in the sample.   

Possible outcomes of the probability that the governor and treasurer are:

GLST, GLAT, GSAT

As a result, a sample that includes the governor and treasurer has a probability of:

$\frac{3}{5}=0.6$

Part (d) Determine the probability that the governor is included in the sample.

Possible outcomes of the probability that the governor and treasurer are:

GLSA, GLST, GLAT, GSAT

As a result, a sample that includes the governor is included in the sample has a probability of:

$\frac{4}{5}=0.8$