A puzzle about inference

Here is a puzzle which I often use as a starter for a course of lectures on probabilistic coupling. The puzzle arose during some research -- I devised it as a simple example to show myself why a particular idea would not work -- and I developed the solution using calculations. In a lunch queue, I asked James Norris of Cambridge whether he could think of a calculation-free answer, and he found one almost immediately.

• You go to Starbucks with a friend.
  
• You are the quiet type, and stay in the front room near the window, sipping a coffee slowly to make it last.
  
• She is extrovert, and has gone through to a further room where the louder people gather.
  There she plays a game: toss n coins, win if r heads or more.
• After the game should have finished, a third friend comes through and says,
  either: "She won the first toss'';
  or: "She won at least one toss''.
  (Why don't people speak more clearly?!)
• Which is better news for your friend? Prove your answer without calculation!

Wilfrid Kendall : 03 Jun 2017 14:24 |  Tags: Coupling Motivation St220 |  Comments (0) |  Report a problem