Questions tagged [probability-theory]
Challenges which involve computing probabilities for random variables and stochastic processes.
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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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Not Your Routine Bean Machine
Consider this ASCII version of a mechanism similar to a bean machine or plinko/pachinko game:
O
^
\ ^
^ ^ \
\ ^ / ^
U U U U U
1 2 3 4 5
The ...
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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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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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Are these dice nontransitive?
Nontransitive dice are nice little toys that defy our intuition in probability theory. We'll need a few definitions for this challenge:
Consider two dice A and B which are thrown at the same time. We ...
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Extreme Whitewater Canoeing
You are paddling a canoe down a fairly fast whitewater river. Suddenly, your paddles explode, and you find yourself in a dangerous situation hurtling down a river rapid without any paddles. Luckily, ...
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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 ...
user9206
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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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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 ...
user45941
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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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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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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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Prepare to... die?
Background
One source of ennui in tabletop role-playing games is dealing with rolls involving many dice. Casting a Disintegration spell may be instantaneous, but rolling and adding together 40 dice ...
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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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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 ...
user9206
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Sample integers that sum to one hundred
Given a positive integer n, randomly output n non negative integers that sum to one hundred. n will be at most 200. The output should be present as a list of integers (not sorted).
Your random sample ...
user108721
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Fix a broken random function
A friend has an add-on card in their computer which generates a perfectly random number from 1 to 5 inclusive. Unfortunately, they spilt cola on it somehow, and it now generates only 2's for all ...
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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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(Somewhat) Pedantic Birthday Paradox
Background
The birthday paradox is a popular problem in probability theory which defies (most people's) mathematical intuition. The problem statement is:
Given N people, what is the probability ...
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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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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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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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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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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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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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Build a program to analyze coin flip sequence choices
In a puzzle in an old book of mine, a game is defined in which two players choose sequences of coin flips that they believe will appear first when a coin is repeatedly flipped. (It was actually odd ...
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Weighted coin flip strings
Given n, k, and p, find the probability that a weighted coin with probability p of heads will flip heads at least k times in a row in n flips, correct to 3 decimal digits after decimal point (changed ...
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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 ...
user7467
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Computer: you do the math
This challenge is partly an algorithms challenge, involves some math and is partly simply a fastest code challenge.
For some positive integer n, consider a ...
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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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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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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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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 ...
user9206
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Uncertainty in the Timeline of a Day
Suppose your alarm wakes you up one morning, but you hit snooze so you can sleep for 8 more minutes. When it rings again you grudgingly get up and take a shower, which you estimate takes 15 to 17 ...
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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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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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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 ...
user9206
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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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Calculate probability of getting half as many heads as coin tosses.
Write a program that, given a small positive even integer from standard input, calculates the probability that flipping that many coins will result in half as many heads.
For example, given 2 coins ...
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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 ...
user9206
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"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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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 ...
user9206
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Random factorized numbers
Input
The code should take an integer \$n\$ between 1 and 1000.
Output
The code should output positive integers with \$n\$ bits. Accompanying each integer should be its full factorization. Each ...
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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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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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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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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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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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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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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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