# Probability of finding a random number in a random interval vs. random samples

Suppose there is a lottery where a random natural number between 1 and n = 1000 is drawn in secret. They sell two different tickets to customers:

• A ticket with k = 10 random numbers on it (not sorted, no repetitions)
• A ticket with an interval of k = 10 succeeding numbers starting at a random offset <= 991

A lot of tickets are sold, so there are expected to be several people with the secret random number put on their ticket. To resolve this, there are two procedures:

• The order of the numbers on the ticket matters. Whoever has the winning number at the lowest position, wins.
• If this did not single out a winner, the prize money is split among all those tickets with the winning number at the lowest position.

Which of the tickets should you buy? Does it matter? I figure that the chance of hitting the winning number is 1/100 in both cases. But what is the probability of taking the money home with you? Intuitively, I would say that both tickets have the same probability to win the same amount of money, i.e. hitting the winning number at a low enough position to get cashed out, but I am a layman in this field.