SOLUTION: 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,

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Question 1105926: 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 38,802,500 Yes
2 Texas 26,956,958 Yes
3 Florida 19,893,297 Yes
4 New York 19,746,227 Yes
5 Illinois 12,880,580 No
6 Pennsylvania 12,787,209 No
7 Ohio 11,459,163 No
8 Georgia 10,097,343 Yes
9 North Carolina 9,943,964 Yes
10 Michigan 9,909,877 No
11 New Jersey 8,938,175 Yes
12 Virginia 8,326,289 Yes
13 Washington 7,061,530 Yes
14 Massachusetts 6,745,408 Yes
15 Arizona 6,731,484 No

Suppose three states are selected at random. Calculate the probability for the following:

a. None of the states selected have a population of more than 9 000 000. (Round your answer to 3 decimal places.)

b. Exactly one of the selected states has a population of more than 9 000 000. (Round your answer to 3 decimal places.)

c. At least one of the selected states has a population of more than 9 000 000. (Round your answer to 3 decimal places.)
Answer by greenestamps(13206) About Me  (Show Source):
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You are selecting 3 of the 15 states in the list, so the denominator of the probability fraction for all three cases is "15 choose 3": C%2815%2C3%29+=+%2815%2A14%2A13%29%2F%283%2A2%2A1%29+=+455.

In all three cases you are looking for states with populations of more than 9 million. 10 of the 15 have populations of more than 9 million; 5 do not.

a) To have none of the three state you choose having populations over 9 million, you need to choose 3 of the 5 states with lower populations (5 choose 3) and none of the 10 with higher populations (10 choose 0).

The probability for this case to 3 decimal places is %28C%285%2C3%29%2AC%2810%2C0%29%29%2FC%2815%2C3%29+=+%2810%2A1%29%2F455+=+.022

b) To have exactly one of the three state you choose having populations over 9 million, you need to choose 2 of the 5 states with lower populations (5 choose 2) and 1 of the 10 with higher populations (10 choose 1).

The probability for this case to 3 decimal places is %28C%285%2C2%29%2A%28C%2810%2C1%29%29%29%2FC%2815%2C3%29+=+%2810%2A10%29%2F455+=+.220

c) This case is just the "opposite" or complement of the first case: "at least one" is the complement of "none". So the probability for this case is 1-.022 = .978.