Questions tagged [probability-theory]
Challenges which involve computing probabilities for random variables and stochastic processes.
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Pick a random string at a fixed edit distance
I have string \$s\$ of length \$n\$ and some constant integer \$k\$ which is at most \$n\$. Give the fastest algorithm to sample a random string with Levenshtein distance \$k\$ from \$s\$ uniformly.
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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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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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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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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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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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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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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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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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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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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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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 ...
user9207
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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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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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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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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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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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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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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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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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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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Frequency Distribution of Multiple Dice Rolls
Given two positive integers a and b, output the frequency distribution of rolling a b-sided ...
user45941
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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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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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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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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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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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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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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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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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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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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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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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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 ...
user45941
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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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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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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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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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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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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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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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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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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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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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"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 ...
- 3,293
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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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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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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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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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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