A probability puzzle from a TV game show challenges contestants to boost their odds beyond the seemingly obvious 25% chance of both guessing correctly.
The Game Setup
The compere announces that at the end of the show, two people will be chosen and each placed in a separate booth. In the booth, each flips a fair coin, out of sight of the other person but visible to the audience. Then each must guess what the other person flipped – heads or tails. If they both guess correctly, they receive a prize.
At first glance, each person has a 50% chance of guessing correctly, so the chance of both guessing correctly is 25%. But is it really that low?
A Surprising Twist
You are 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?
Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam and author of several books on probability, contributed today's puzzle.
Hint and Discussion
The answer will be provided at 5pm UK time. Readers are encouraged to discuss their favorite game shows without spoiling the solution.
