Question

The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county

Answer 1

`\frac{159^(n) -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^(n) }`

Explanation:

number of counties = 159

n number of people are mutually independent and equally likely home locations

considering the details given in the question

n ≤ 159

The number of ways for people ( n ) will live in the different counties (159) can be determined as
`(\left \{ {{159} \atop {n}} \right} )`

since the residents are mutually independent and equally likely home locations hence there are :
`159^(n)` ways for the residents to live in

therefore the probability =
`\frac{159^(n) -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^(n) }`