Question

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

1. None of the states selected have a population of more than 9,000,000

Answer 1

Number of states with population less than 9,000,000 are 5 out of the total 15 states

Number of ways of selecting 4 states from total 15 states = = 15C4 = 15 ! / [ 4! * (15-4)! ]

= 15 ! / [ 4! * 11 ! ]

= 1365

Now we need to select 4 states from the 5 states that have population less than 9,000,000 which can be done in

   = 5C4 = 5! / [ 4! * (5-4)! ]

= 5

So Probability that one of the states selected have a population of more than 9,000,000 = 5 / 1365

= 0.003663

So Probability that one of the states selected have a population of more than 9,000,000 = 0.003663