# Questions tagged [coin-tossing]

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

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117 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 ...
201 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 ...
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 ...
948 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. ...
305 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 ...
485 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 ...
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?
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 ...
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 ...
889 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 ...
561 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 ...
380 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 ...
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 ...
566 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 ...
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 ...
612 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 ...
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 ...
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, ...