Daily Maths Challenges

195 readers

1 users here now

Share your cool maths problems.

Complete a challenge:

Post your solution in comments, if it is exactly the same as OP's solution, let us know.
Have fun.

Post a challenge:

Doesn't have to be original, as long as it is not a duplicate.
Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
Optionally include solution in comments, let it be clear this is not a homework help forums.
Tag [unsolved] if you don't have a solution yet.
Please include images, if your question includes complex symbols, attach a render of the maths.

Feel free to contribute to a series by DMing the OP, or start your own challenge series.

founded 6 months ago

MODERATORS

siriusmart@lemmy.world

Coin-flipping game (lemmy.world)

submitted 6 months ago* (last edited 6 months ago) by zkfcfbzr@lemmy.world to c/dailymaths@lemmy.world

12 comments fedilink hide all child comments

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?

you are viewing a single comment's thread
view the rest of the comments

[–] zkfcfbzr@lemmy.world 5 points 6 months ago* (last edited 6 months ago) (1 children)

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 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. ;)