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Questions tagged [coin-tossing]

A puzzle about flipping/tossing coins. Typical examples are about the probability that head or tail comes out.

1
vote
1answer
110 views

Guess the coin toss [duplicate]

You and your friend are put in two different rooms with just a coin and no way to communicate. You both toss the coin at the same time. Your task is for at least one of you to guess correctly what ...
5
votes
0answers
199 views

Truly Fair Coin [closed]

Is there such a coin – or cylinder – in which there is an equal chance of getting heads, tails or landing on its side? I am guessing that it is a ratio between the radius and height of the coin, but ...
13
votes
10answers
2k views

Frequentists be damned! Design an evil coin to prove a point [closed]

The frequentists' definition of a "fair coin" is a coin that, tossed a million times, converges toward an equal number of heads and tails. But what is meant by converges? We might imagine a plot of ...
0
votes
1answer
884 views

100 coins (Heads and Tails) [duplicate]

"You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. ...
6
votes
2answers
298 views

More coin flipping

After their last game, Alice and Bob decide to have a bit more fun with their fair coin. Bob proposes the following game: considering a flip can come out as heads or tails, they will both predict one ...
8
votes
2answers
459 views

The asymmetric coin game

After finding a coin in her farm, Alice proposes the following game to Bob: Alice will flip the coin $n$ times. Bob will then flip the coin $2n$ times. If Bob manages to get the same amount of ...
7
votes
3answers
1k views

No two heads in a row

Suppose I toss a fair coin a 100 times. What is the probability of not getting two heads in a row?
10
votes
5answers
2k views

Unfair coins at South Park Elementary v2

Following Unfair coins at South Park Elementary Wendy and Sally have another friend, called Timmy. Although Timmy has no coin, he wants to play this game in a fair condition with them. Wendy does the ...
15
votes
8answers
5k views

Unfair coins at South Park Elementary

Wendy Testaburger and Sally Turner play a game with two unfair coins. A coin flip with Wendy's coin shows head with probability $\frac {1} {100}$. A coin flip with Sally's coin shows head with ...
13
votes
5answers
882 views

Seven cowboys play a coin tossing game [closed]

Seven cowboys play a coin tossing game with a fair coin where each player has a chance of 1/2 of winning. Each of them plays once against all other six. What is the probability that each cowboy wins ...
2
votes
3answers
553 views

What is the value of this other coin flipping game?

This is variation of this question: What is the value of this coin flipping game? Imagine that you can play the game in a casino - you are flipping a fair coin. If you get tails, the game continues ...
6
votes
4answers
379 views

Drawing uniformly using a single biased coin

Your task is to draw uniformly from a set of size $N$. You are given a single coin which you can ‘bend’ to control the probability $p\in[0,1]$ of throwing a Head, but you are only allowed a bounded ...
4
votes
2answers
1k views

A coin flip's long tail

I have a (possibly-) unfair coin, which lands heads with probability $p$ and lands tails with probability $1-p$. I toss it twice; the tosses are independent and identically distributed. The ...
6
votes
2answers
545 views

A jar of mixed coins [closed]

This is a slight adaptation of a google interview question that I found entertaining. You are given a jar with N coins, K of them are fair. The remaining coins have heads on both sides. You choose a ...
9
votes
6answers
2k views

Two men for one gold coin

Two men find an old gold coin and want to have a coin toss with it to decide who gets it. The only problem is the coin is heavier on one side so it comes up heads more than tails. What is a fair way ...
12
votes
6answers
605 views

Flipping a randomly-lopsided coin

Whenever the Lopsided Mint stamps a coin, its heads-bias $p$ is chosen uniformly at random between $0$ to $1$, which makes it have a probability $p$ of landing heads when flipped. Bob takes a random ...
-9
votes
1answer
1k views

Coins, Dice, and Probability! [closed]

Background: It's time for a little bit of fun, your friends are playing a game and you decide to join them! Gamplay: You each sit down and play on a flat surface. You sit in a circle and each throw ...
15
votes
4answers
1k views

Another probabilistic coin puzzle

Credit to GOTO0 for the original idea for this puzzle, which is the converse of his puzzle. In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, ...
54
votes
3answers
5k views

Left coin, right coin, last coin?

In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put them on the table in front of them. Then each ...
19
votes
5answers
7k views

Flip a Fair Coin

I found this question and became curious, can anyone tell me the answer and prove it, i know it seems fairly simple but just thought an explanation of this would make an interesting case. Flip a fair ...