Listed below is the population by state for the 15 states with the largest population. Also included is whether that state's border touches the Gulf of Mexico, the Atlantic Ocean, or the Pacific Ocean (coastline).

Rank

State

Population

Coastline

1

California

36,553,215

Yes

2

Texas

23,904,380

Yes

3

New York

19,297,729

Yes

4

Florida

18,251,243

Yes

5

Illinois

12,852,548

No

6

Pennsylvania

12,432,792

No

7

Ohio

11,466,917

No

8

Micigan

10,071,822

No

9

Georgia

9,544,750

Yes

10

North Carolina

9,061,032

Yes

11

New Jersey

8,685,920

Yes

12

Virgina

7,712,091

Yes

13

Washington

6,468,424

Yes

14

Massachusetts

6,449,755

Yes

15

Indiana

6,345,289

No

Note 5 of the 15 states do not have a coastline. Suppose three states are selected at random. What is the probability that

i) None of the states selected has any coastline?

ii) Exactly one of the selected states has a coastline?

iii) At least one of the selected states has a coastline?

In addition to finding the above probabilities, comment on the distribution you applied to get the probabilities. Discuss whether assumptions for the distribution are met by the scenario in the given problem.