Shown here are the top 10 U.S. cities ranked by number of rooms sold in a recent

ID: 3181026 • Letter: S

Question

Shown here are the top 10 U.S. cities ranked by number of rooms sold in a recent year.

Rank City Number of Rooms Sold

1 Las Vegas (NV) 40,000,000

2 Orlando (FL) 27,200,000

3 Los Angeles (CA) 25,500,000

4 Chicago (IL) 24,800,000

5 New York City (NY) 23,900,000

6 Washington (DC) 22,800,000

7 Atlanta (GA) 21,500,000

8 Dallas (TX) 15,900,000

9 Houston (TX) 14,500,000

10 San Diego (CA) 14,200,000

Suppose four of these cities are selected randomly.

What is the probability that exactly two cities are in California?

What is the probability that none of the cities is east of the Mississippi River?

What is the probability that exactly three of the cities are ones with more than 24 million rooms sold?

a)Probability exactly two cities are in California:

Total number selecting 4 cities from 10=10C4

There are two cities from california number of ways selecting them 2C2=1 & and the remaining 2 cities can from remaining 8=8C2

Probability=(8C2*1)/(10C4)=2/15.

b)As I not from US i dont know what cities are to east of mississipi

If X cities are to east of mississipi exclude them you have to select from 10-X

So prob=((10-X)C4)/10C4.

c)there are 4 cities in which above 24 million rooms are sold.So we have to select 3 from them

4C3 and also 1 from rest 6=6C1.

So prob=(4C3*6C1)/(10C4)=4/35.

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