Coin-flipping game (lemmy.world)

submitted 7 months ago* (last edited 7 months ago) by zkfcfbzr@lemmy.world to c/dailymaths@lemmy.world

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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?

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[-] zkfcfbzr@lemmy.world 5 points 7 months ago* (last edited 7 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@sh.itjust.works 3 points 7 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. ;)

this post was submitted on 22 May 2024

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