We’re playing a game. I flip a coin. If it lands on Tails, I flip it again. If it lands on Heads, the game ends.

You win if the game ends on an even turn, and lose otherwise.

Define the following events:

A: You win the game

B: The game goes on for at least 4 turns

C: The game goes on for at least 5 turns

What are P(A), P(B), and P(C)? Are A and B independent? How about A and C?

  • zkfcfbzrOPEnglish
    5•6 months ago

    Games are always played to completion, though if you wanna make it (barely) more challenging you can add in a 5% chance for both players to get bored and give up on each round (before flipping), leading to a loss. Though it seems unlikely - after flipping a quarter 20 times and getting Tails every time, I’d be inclined to keep flipping if anything.

    response

    These are correct. It is possible to reason out which of B and C is independent of A without going into the numbers.

    • enkers
      3•6 months ago

      after flipping a quarter 20 times and getting Tails every time, I’d be inclined to keep flipping if anything.

      It’s a sunk cost fallacy, it’s never too late to get bored and give up. ;)