- Players in a game show booth will each flip a coin and guess the other’s result.
- A strategy exists that increases their chances of winning above 25%.
- The solution involves communicating before the game starts.
- Professor Henk Tijms provided this puzzle, an expert on probability.
The Game Show Scenario
Today’s puzzle imagines a TV game show hosted by a compere who announces that at the end of the show two individuals will be chosen and each placed in a separate booth. In the booth, each of them will flip a fair coin, out of sight of the other person but visible to the audience. Then each of them must guess what the other person flipped – heads or tails. If they both guess correctly, they receive a prize.
The basic probability for guessing correctly is 50 per cent for each individual. Thus, the chance that both will guess correctly by random chance is 25 per cent. Or is it? You’re in the studio watching the show, and to your surprise, you and your friend are called up to play the game. As you walk up to the stage, you whisper a strategy to your companion that gives you a better than 25% chance of winning the prize. What is this strategy, and what is the probability of winning? I’ll be back at 5pm UK with the answers.
Professor Henk Tijms' Puzzle
This puzzle has been part of a regular column where Professor Henk Tijms, an Emeritus Professor of Operations Research at VU Amsterdam and the author of several books on probability, invites suggestions for future challenges. He has been setting puzzles in this column every alternate Monday since 2015. If you have any favorite game shows or puzzles to share, feel free to suggest them by emailing Henk Tijms.
Stay tuned for further challenges and engage with the community to discuss your favorite game shows or any other interesting topics related to probability.
Source: The Guardian
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