Questions tagged [probability-theory]
Challenges which involve computing probabilities for random variables and stochastic processes.
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Odds for second smallest prime factor
Given a prime number \$p\$ output the asymptotic density of the set of positive integers which have \$p\$ as their second-smallest distinct prime factor
Input/Output
Input: one of the following ...
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Avoiding Loops!
Given a collection of coloured laces, what would be the probability, \$P\$, that Alice won't create any loops if, until impossible, they tie two uniformly chosen, free lace ends of differing colours ...
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Compute probability of seeing all the balls
Given \$x\$ distinguishable balls (say they have different colors), sample with replacement repeatedly until all the balls that have been seen, have been seen at least twice.
Challenge
The input is ...
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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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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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