A lottery sells 10,000 tickets and awards 10 prizes. If you buy one ticket, what is the probability that you do not win a prize?

Introduction / Context:
In a finite uniform lottery, the probability of winning equals the number of prize tickets divided by total tickets. The probability of not winning is the complement.

Given Data / Assumptions:

• Total tickets = 10,000.
• Prizes = 10.
• One ticket purchased; each ticket is equally likely to be drawn as a prize.

Concept / Approach:
P(no prize) = 1 − P(prize) = 1 − (prize tickets / total tickets).

Step-by-Step Solution:
P(prize) = 10 / 10000 = 1 / 1000.Therefore, P(no prize) = 1 − 1/1000 = 999/1000.

Verification / Alternative check:
Non-prize tickets = 10000 − 10 = 9990. For one ticket chosen uniformly, P(no prize) = 9990/10000 = 999/1000 after simplification.

Why Other Options Are Wrong:
9999/10000 would correspond to 1 prize; 9/10 ignores the precise counts; 1/1000 is P(win), not P(no win).

Common Pitfalls:
Mixing up the probability of winning with not winning; not simplifying to lowest terms.

Final Answer:
999/1000