A statistically fair probability method that the TV channel's management could use to determine the winner among the 5,000 entries is a **random drawing**. Here's how it works:
1. Assign a unique identification number (e.g., a serial number) to each entry, numbering them from 1 to 5,000.
2. Use a random number generator, like a computer-based random number generator or a physical drawing mechanism, to select a single random number within the range of 1 to 5,000.
3. The entry corresponding to the randomly selected number becomes the winner of the contest and receives the gift vouchers and the free international cruise.
Statistically, this method is fair because each entry has an equal and random chance of being selected as the winner. No one can predict or control the outcome, and all entries are treated impartially.
However, the question of whether it's morally fair that each entry gets an equal opportunity of winning can be subjective. Some argue that this method is morally fair because it ensures that everyone has an equal chance, regardless of their background or circumstances. Others might argue that it's not morally fair if certain entries were obtained through unethical means or if some participants have more significant needs than others.
Ultimately, the morality of such a contest depends on the specific context, rules, and ethical considerations of the situation. To ensure moral fairness, it's essential for the TV channel to have clear and transparent contest rules and to conduct the drawing in an unbiased manner.