Today's Puzzle: A TV Game Show Scenario
The host announces that by the end of the show, two contestants will be selected and placed in separate booths.
Inside each booth, the contestant will flip a fair coin, unseen by the other player but visible to the audience.
Each contestant must then guess the result of the other person's coin flip—heads or tails. If both guess correctly, they win a prize.
The probability of each contestant guessing correctly is 50%. Consequently, the chance that both guess correctly is 25%.
You are in the studio watching the show, and unexpectedly, you and a friend are called to participate. As you approach the stage, you quietly share a strategy with your companion that improves your chances of winning beyond 25%. What is this strategy, and what is the probability of winning?
I will return at 5pm UK time with the answers.
PLEASE NO SPOILERS – discuss your favourite game shows. (Real or imaginary.)
Thanks to Henk Tijms for today's puzzle. Henk is Emeritus Professor of Operations Research at VU Amsterdam and the author of several books on probability.
Since 2015, I have been posting puzzles here on alternate Mondays and am always seeking excellent puzzles. If you would like to suggest one, please email me.
