This problem was posed to me by a student (whose name has been altered here). I remixed it into this challenging probability puzzle. Good luck!
Spice Level: 🔥🔥🔥🔥⚪
Field of Math: Probability
Kiran’s Karnival offers a simple coin flipping game. Here are the rules:
- Flip a coin
○ If it’s heads, return to step 1 and flip again
○ If it’s tails, end the game
The game costs $3 to play, but you get paid $1 per coin flip. For example, if you get all heads until your 5th flip is tails, you get $2, because you paid $3 and earned $5. However, if your second flip is tails, you lose $1. First, explain why this game is not fair for the player. Then, propose one change to the rules of the game to make it fair.
Note that in a fair game, if you play enough times, you and the carnival should come out close to even.