Expected Number of Age-Matching Cards in a Set of 1000

[succubus]

A set of 1000 cards, numbered 1 through 1000 are distributed among 1000 people. Compute the expected number of cards that are given to people whose age matches the number on the card.


So the relevant formula is expected value, but its conditioned because of the ages. So I assumed that the age range was between 1-100.
So n* P{card reads age | age <= 100)

Is this the correct assumption?

So would the probability be 1/1000 / 100/1000 = .01

 

[Billy Bob]

The answer is 1.

Hints:

Consider the random variable N_i = number of people age i who get a card with their age.

We want E(N_1 + N_2 + ... + N_1000).