Two movies—Movie X and Movie Y—are tied in a vote for what to watch. The group wants a fair tie-breaker, meaning each movie has probability of being chosen. Which procedure is fair?
- Flip a fair coin: heads means Movie X, tails means Movie Y. (correct answer)
- Roll a standard die: 1–4 means Movie X and 5–6 means Movie Y.
- Choose the movie that came out earlier so both movies eventually get a turn.
- Write both titles on slips of paper, but fold Movie X's slip twice and Movie Y's slip once before drawing.
Explanation: The skill here is using probability to make fair decisions. Fairness means that each movie has an equal probability of being selected, specifically 1/2 for Movie X and Movie Y. In the correct method, a fair coin is flipped once, with heads for Movie X and tails for Movie Y. This assigns equal chances because the coin has two equally likely sides, so each movie has a probability of 1/2. One incorrect method is rolling a die where 1–4 means Movie X and 5–6 means Movie Y, introducing bias by giving Movie X a probability of 2/3 and Movie Y only 1/3. Remember, fairness is about equal chances in each selection, not about the same movie being chosen equally often over multiple selections. To apply this strategy elsewhere, list all possible outcomes and check if each option is equally likely.