Questions tagged [probability-theory]

Challenges which involve computing probabilities for random variables and stochastic processes.

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Calculate the probability of getting this hand in n tries [closed]

Imagine there is a card game where the primary objective of the game is to get 4 of one card in your hand. Game mechanics Each player starts of with 10 cards in their hand. The remaining 32 cards (...
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3 votes
7 answers
724 views

Yet another coin flipping problem

Problem Starting with a set of 10 coins at the start where all coins are tails up, and given n number of integers \$x_1, x_2, x_3... x_n\$ representing n rounds of coin flipping. At each round, we ...
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3 votes
2 answers
195 views

A Suitable Mission — The Professor's Revenge

Summer Klerance turned in her term assignment for this challenge. Her professor was miffed (but also amused) when he overheard a disgruntled classmate of Summer's saying she got her answers by ...
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  • 616
8 votes
7 answers
451 views

A Suitable Mission

Summer Klerance, a senior in college, is what her teachers refer to as GBL*. Students in her probability class have been assigned individual problems to work on and turn in as part of their final ...
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  • 616
5 votes
10 answers
1k views

Odds that a string of N digits contains two or more of the same

I have to fill in 2fa codes all day. They're 6-digit strings. One day I noticed that not once did any of these codes contain 6 unique digits, like 198532 There was always at least one double, like ...
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  • 1,276
13 votes
11 answers
2k views

Calculate the probability of getting to the target first (exactly)

Consider the following probability puzzle. We start with a string of bits all set to 0. At each step we choose a bit uniformly and independently at random and flip it. The value your code has to ...
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18 votes
14 answers
2k views

Lucky dice rolls

Lucky dice rolls In pen and paper roleplaying games dice are used for various chance calculations. The usual way to describe a roll is \$n\textbf{d}k\$ where \$n\$ is the number of dice and \$k\$ is ...
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21 votes
15 answers
1k views

Penney-Conway odds

Background Penney's game is a two-player game about coin tossing. Player A announces a sequence of heads and tails of length \$n\$, then player B selects a different sequence of same length. The ...
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2 votes
1 answer
256 views

Estimate the mean minimum Hamming distance

Task Inputs \$b \leq 100\$ and \$n \geq 2\$. Consider \$n\$ binary strings, each of length \$b\$ sampled uniformly and independently. We would like to compute the expected minimum Hamming distance ...
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16 votes
13 answers
2k views

Probabilistically fair prize splitting for two-player coin toss

Introduction Adam (A) and Bubbler (B) are playing coin toss, where the one who wins 5 times first would win the prize of $32. If the game is aborted when the scores are ...
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  • 62.1k
6 votes
12 answers
320 views

Probabilistic approach puzzle

A few hours earlier, I got this puzzle: Suppose, you toss a coin n times, then what is the probability of getting m number of heads? ( where m belongs to the set of all prime numbers) For instance,...
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  • 2,850
13 votes
2 answers
382 views

Pólya urn flip and roll

Problem statement Pólya is playing about with his urn again and he wants you to help him calculate some probabilities. In this urn experiment Pólya has an urn which initially contains 1 red and 1 blue ...
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5 votes
7 answers
278 views

Choose the Most Dramatic Outcome

The premise of this is simple: A 10% chance is pretty unlikely, but everyone knows that a one-in-a-million chance is a sure thing! So, write code that implements the following "dramatic" probability ...
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  • 3,566
6 votes
5 answers
429 views

Watch the bookie win

When you roll a die, you have a 6:1 chance of any given option. There's a bookmaker taking bets on die rolls. He owns £20 at the start of the game. The bookmaker offers odds of 4:1, but gamblers ...
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  • 11.1k
23 votes
24 answers
2k views

Sample the Pareto Distribution

The Pareto Distribution is a probability distribution that comes up a lot in nature. It has lots of special properties, such as an infinite mean. In this challenge, you will output a number sampled ...
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24 votes
22 answers
2k views

Frequency Distribution of Mixed Dice Rolls

A follow-up to this challenge Given a set of mixed dice, output the frequency distribution of rolling all of them and summing the rolled numbers on each die. For example, consider ...
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20 votes
9 answers
804 views

Hand patterns in a card game

A deck of cards is the Cartesian product of S suits and R ranks. Many, though not all, card games use ...
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  • 14.5k
20 votes
8 answers
980 views

Pick-flatten a list

Consider the process of "picking" a nested list. Picking is defined as follows: If the argument is a list, take an element from the list at random (uniformly), and pick from that. If the argument is ...
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23 votes
22 answers
2k views

Frequency Distribution of Multiple Dice Rolls

Given two positive integers a and b, output the frequency distribution of rolling a b-sided ...
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49 votes
29 answers
11k views

What an Odd Function

Your task here will be to implement a function1 that forms a permutation on the positive integers (A bijection from the positive integers onto themselves). This means that each positive integer ...
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  • 84.7k
26 votes
3 answers
647 views

A lean, mean bean machine

A classic example to introduce people to the concept of a discrete probability distribution is the bean machine. This machine has a large amount of marbles fall from a narrow passageway at the top, ...
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8 votes
3 answers
348 views

Golfception arrives

Lets play golf while we golf. Problem: Distance to the hole initially is 700m Each hit to the ball will make it advance to the hole 250-350m, this should be random. Each hit has a 5% probabilities ...
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3 votes
9 answers
325 views

The most unreliable gun ever [duplicate]

You are given a very special gun with a full magazine. Let n be the initial number of bullets in the magazine and i the number ...
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  • 437
11 votes
5 answers
4k views

Plot the Gaussian Distribution in 3D

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural ...
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16 votes
25 answers
2k views

Sums of 100 Rolls of Two Six Sided Dice

Suppose you have two six-sided dice. Roll the pair 100 times, calculating the sum of each pair. Print out the number of times each sum occurred. If a sum was never rolled, you must include a zero or ...
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2 votes
2 answers
174 views

Random subset generator [closed]

Randomly choose one out of k-length, ordered subset of characters in a string, while only storing a limited number of characters. The subset must be chosen with ...
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26 votes
35 answers
8k views

Pick a random number between 0 and n using a constant source of randomness

Task Given a positive integer n less than 2^30 specified as input in any way you choose, your code should output a random ...
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20 votes
7 answers
2k views

Sample a random non-decreasing sequence

Input: Two integers n and k given in any form that is convenient for your code Output A random non-decreasing sequence of k integers, each in the range 1 to n. The sample should be chosen uniformly ...
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12 votes
4 answers
602 views

Code golf a random orthogonal matrix

An orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors). This means that M^T M = I, where I is the identity matrix ...
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18 votes
16 answers
985 views

Probability of All Combinations of Given Events

Given a sequences of events with probabilities between 0.0 and 1.0, generate and derive the probability of each combination occurring. You may presume that a sequence of numbers is provided in ...
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12 votes
3 answers
504 views

Generalized Birthday Problem

Tonight, my fiancée took me out to dinner to celebrate my birthday. While we were out, I heard Happy Birthday sung to 5 different guests (including myself), in a restaurant full of 50 people. This got ...
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11 votes
3 answers
431 views

What's the chance that I'll win a door prize?

My local ACM chapter gives out door prizes to people who come to the meetings. You get an increased chance of winning if you solve the programming puzzle, however (but I always solve that puzzle). ...
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  • 20.9k
10 votes
15 answers
1k views

Probability of something happening at least n out of m times

Write a program or function, that given a success probability p, a number n and a number of trials m returns the chance of at least n successes out of m trials. Your answer must be precise to at ...
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  • 38.6k
18 votes
20 answers
1k views

Compute the histogram entropy estimation of a string

Write a program or function that estimates the Shannon entropy of a given string. If a string has n characters, d distinct characters, xi is the i th distinct character, and P(xi) is the probability ...
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  • 38.6k
6 votes
1 answer
285 views

Model a probability table using 15-bit fixed probabilities

A histogram is an array of integers that counts the number of times a symbol occurs. For example, for the string "aaabbbabbdebabbbebebdbaaabbabaaaaeebeaabaaba" a ...
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  • 38.6k
32 votes
28 answers
7k views

Choose The Powerball Numbers!

Powerball is an American lottery that has recently gained attention because the current jackpot (as of January 11, 2016) is the largest lotto prize in history, at about $1.5 billion (USD). Powerball ...
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9 votes
2 answers
194 views

Talent rolls in DSA

Some friends and I have played some DSA (a mainly german tabletop RPG much like D&D). I was wondering what the chance on passing rolls are, so you will have to write some code to calculate it. ...
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  • 2,565
8 votes
6 answers
291 views

Card pair probability

Given a deck consisting of N copies of cards with integer values [1,M] for a total of N*M cards, compute the probability that a card with the value of 1 is adjacent to a card with the value of 2. ...
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32 votes
47 answers
3k views

1/N probability

Because there are not enough simple code-golf challenges: Create an optionally unnamed program or function that, given (by any means) an integer 1 ≤ N ≤ 10000, outputs your language's True value with ...
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  • 27.1k
7 votes
3 answers
337 views

Guess the hidden communities

Background This challenge is about the stochastic block model. Basically, you are given an undirected graph, where the nodes represent people, and the edges represent social connections between them. ...
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  • 42k
16 votes
6 answers
569 views

Who's that probability distribution?

Introduction In this challenge, you are given a list of nonnegative floating point numbers drawn independently from some probability distribution. Your task is to infer that distribution from the ...
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  • 42k
10 votes
11 answers
2k views

"i" have "i" chance of occuring

Design a random number generator where the i th number has i% chance of occurring for all 0 < i < 14. 0 should have exactly 9% chance of occurring. The seed for the generator should be the ...
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8 votes
6 answers
334 views

Implement an API for probability distributions

Introduction In this challenge, your task is to implement a collection of simple functions that together form a usable mini-library for simple probability distributions. To accommodate some of the ...
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  • 42k
7 votes
2 answers
283 views

Probability to clear the board or win

In the game Hearthstone there is a playing board containing friendly and enemy minions, and two heroes - yours and the enemy's. To generalize and simplify, we will assume it's your turn, the opponent ...
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  • 38.6k
7 votes
2 answers
314 views

Simple single-player board game, expected score distribution

This is the first problem I've posted here; please post criticisms in comments. Summary A game board consists of a starting space, an ending space, and between them are ...
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  • 171
9 votes
1 answer
340 views

Knockout probabilities

Knockout is a basketball game where players take turns shooting. It is played as a sequence of two-player contests, each of which has the possibility of "knocking out" one of those players. Suppose ...
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  • 4,404
10 votes
2 answers
894 views

Probabilities - how high can you go?

I previously asked a question for how to compute a probability quickly and accurately. However, evidently it was too easy as a closed form solution was given! Here is a more difficult version. This ...
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10 votes
5 answers
1k views

Calculate a probability exactly and quickly

[This is a partner question to Calculate a probability exactly ] This task is about writing code to compute a probability exactly and quickly. The output should be a precise probability written as a ...
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9 votes
4 answers
1k views

Calculate a probability exactly

This task is about writing code to compute a probability exactly. The output should be a precise probability written as a fraction in its most reduced form. That is it should never output ...
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13 votes
1 answer
882 views

XKCD Bracket Probabilities

Today's XKCD is a sports-tournament style bracket, where the contestants are well-known names, put into groups of possibly confusing names. Give the probability that a given contestant will win the ...
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