Final answer:
The probability of not winning a prize in a lottery where 10,000 tickets are sold and ten are winners is determined by subtracting the probability of winning from 1 for one ticket, and raising this probability to the power of the number of tickets bought for multiple tickets, assuming each draw is independent.
Step-by-step explanation:
The subject of this question is probability, which falls under Mathematics. In the described lottery where 10,000 tickets are sold and ten equal prizes are to be awarded, calculating the probability of not winning a prize can be approached using basic probability principles.
- For one ticket: The probability of winning with one ticket is 10/10,000, so the probability of not winning is 1 - (10/10,000) = 9,990/10,000.
- For two tickets: This is not as straightforward as it seems because the two events are not independent (winning with one ticket affects the chances of the next). However, for simplicity, assuming tickets are replaced after each draw (making them independent), then the probability of not winning with either is (9,990/10,000) × (9,990/10,000).
- For 10 tickets: Similarly, if we consider independent events, the probability of not winning with any of the 10 tickets is (9,990/10,000)^10.