116 posts tagged with probability.
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How to accurately determine if a random method is indeed random?
I wanted to do a project where I measured how random the native RNGs are in various programming languages. How can I objectively measure my results? Also, if you run a random number generate say 100 vs 10,000,000 times should the distribution even out the more tests you run?
How to maximize my chances of passing?
Does anyone have any tips or tricks for making the most out of my study time and/or keeping myself in the right headspace for exams for a must-pass class? [more inside]
Math: Probability and combinatronics
Ok... so I'm looking at a candidate for a job position and I notice on his resume the following:
Between his mobile number and my mobile number (10 digit, US format) there are 9 numbers in common, 5 of which are in the right position. [more inside]
How many pairs in a deck drawn two cards at a time?
I shuffle a deck of 52 regular playing cards. I draw two cards, then another two, then another two. I don't return any cards to the deck. If the two cards I draw match in value, they're a pair and I set them to one side. By the time I finish the deck, how many pairs can I expect to have?
A Star Trek-referencing short story about hot beverages and probability
I'm trying to find a short story for a friend. It's about a hacked hot-beverages machine in a research facility, and one line references Picard's famous order, "Tea, Earl Grey, hot." More details inside. [more inside]
Card deck probability distribution with reshuffles?
What is the probability distribution (??) of card deals in a deck if the deck is reshuffled before the end is reached? [more inside]
How to calculate probability three things will be on same day of week?
If I know Event 1 will happen three times in a week, Event 2 will happen four times, and Event 3 twice, how can I tell how likely they will be to happen on the same day (assuming they're random)? [more inside]
Real-life based math problem
On my daily commute back home, I drive past ~15 gas stations. In my country, gas prices change daily and vary a bit from one station to the next. So that got me thinking: What would be the best method to decide whether to fill your tank on the station you're currently in front of or lose the current price forever and take your chances on the remaining stations? Assume each station sets their daily price randomly (but they are all within a $1 range), and we start with the reference of the price we paid last time.
Note: I can easily keep track of the lowest price on my way to work and then fill up on the way home, but I am more interested in the math problem than the practical issue.
Let me not neglect that base rate....
Estimating base rates from small sample sizes -- how large a sample do I need to reliably (confidently?) establish the base rate? [more inside]
Fun, visual ways to give students a 1:4 probability
My students will take 4 quizzes. To prepare for each quiz, I will allow them to fill one index card with notes or formulas that they will have a 1 in 4 chance of being able to use during the quiz. Just the act of writing down notes concise enough to fit on a card helps students organize and prepare very well, but they are more motivated to use this method with an incentive. I picked giving them a 1:4 probability of being able to use their notecard during the quiz, making it 'open note,' and am now brainstorming fun ways to carry this out.
I could do a double coin flip, where either heads or tails is called, and two coins have to display what was called. Or I thought about filling 4 beakers full of water and adding food coloring to one and then covering them and getting someone to randomly pick one.
Any other fun things I could try?
Help me figure out what's up with this probability question
Someone posted a probability question on Mastodon: "A, B and C toot the truth with a probability of 1/3 and lie with a probability of 2/3. A makes a toot and B toots an observation on whether or not A was tooting the truth or not. C toots that B confirmed A was truthful. What is the actual probability that A's toot was truthful?" Either I made it more complicated than it needs to be, or a lot of other people are wrong, and I suspect the former. Help me get to the bottom of this! [more inside]
Is This Bathroom Occupied?
The other week there was a puzzle on FiveThirtyEight about the probability of the sign on a bathroom being correct given the behavior of different people in an office (solution). Can you help me figure out why my approach doesn't work? [more inside]
Blundering around in statistics
I am trying to understand some statistical data in a piece dealing with a historical text corpus and am in over my depth, which doesn’t take much doing. I’d be grateful for a simple explanation of what’s going on, plus the technical terms for this phenomenon, if it is one. [more inside]
Too Many Strata To Sample
I have multiple independent variables that I want to stratify my sampling across, but the result would be way more strata than I can sample. Is there a way to stratify across different character states for each independent variable without creating strata for the interactions of each? Example inside. [more inside]
Can you figure out the probability of a specific outcome?
I work in a field where we think about possibly dangerous people. If Mr. X is a poor driver and has a 5% chance of running a red light in the next month, can you know the probability of him running a red light at a specific intersection? Can you know a range of probabilities for that specific intersection? What if it's the intersection that he drives through most often? I think this likely has an easy answer but none of us can clearly explain it so we keep talking about it.
Statistical framing of the engineering and extremism article
Reading this article on the blue got me thinking about conditional probabilities, prediction and causality. I came up with an analytical framing of what I think the article is saying and would be grateful if stats/social science Mefites could tell me if it seems accurate or else set me right. [more inside]
How often to roll 2d6 a special way to guarantee an outcome once?
There is an 8/36 chance that a very particular outcome can be generated by rolling 2d6 in a particular way (both described after the jump). How many times do I need to roll to be certain that this outcome occurs (ie, I can stop rolling)? How about 90 per cent certain? 80 per cent? [more inside]
Probability and choice
I was reading a book on probability and decision making several years ago and it mentioned a rule of sorts that could be used when making a selection from a sample that would help you make an efficient decision that was likely to gave a good outcome. [more inside]
How to Math
I'm a computer science major in college. I'm not a freakin' genius, but I do well-- get A's in my classes, good with abstraction (e.g. pointers), etc. However, I seem to have missed... my entire high school pre-Calculus math curriculum? I don't know. [more inside]
Calculating the probability of a scenario that might happen by chance
I have to validate some input for a database, and I want to present the user with a mathematically accurate estimate of the percentage of data that they entered which may be invalid. The problem is that valid data looks like invalid data 10% of the time. [more inside]
Probability distributions and their practical applications
I am looking for a resource that lists probability distributions and their common real-world applications. For example, I'd expect to see: Lognormal - daily returns in the stock market. Poisson - failure rates for mechanical equipment, ... [more inside]
Predictive analytics basics for programmers?
I'm looking for resources that discuss the basics of data mining and building predictive models. [more inside]
Best or most appropriate Statistic method to Use.
I have a statistics and/or probability question and the last time I took a statistics class Vanilla Ice and Andrew "Dice Clay" were multi-millionaires.
I am not looking for a problem to be solved, I am asking what statistical technique should I use to determine if a time series of data is due to randomness or not. [more inside]
Statistics are hard.
How do you calculate the probability of something when it's not as simple as "do it a bunch of times"? Specifics inside. [more inside]
Fruit salad for statisticians
What formula do I need to determine the probability that a set of size N contains two elements, each appearing with a specific frequency? [more inside]
Travel 5 weeks before wife’s due date? Chances of missing the birth?
I'm thinking about being a away for a week, around 4-5 weeks before my wife's due date. I'm looking hard statistics (chances of missing the birth) and soft advice (what would you do) to help with this decision. [more inside]
Math Problem
Please help with this probability related math problem. [more inside]
Math / probability question re: HIV
I'm trying to calculate the probability of contracting HIV for the husband of an infected woman.
Given a risk of 10-50 conversions per 10,000 exposures. And assuming an average frequency of sexual acts of 2-3 X per week. That's 100-150 sexual acts /year. That should give about a 10%-15% yearly risk of contracting HIV, right?
Has a major lottery ever produced a result that doesn't look random?
Every outcome in a fair lottery is equally probable, yet some results display obvious patterns and feel less likely to the statistically uninformed. Nobody would blink if a six-number lotto draw came up with (3,12,27,31,40,44), but a result of (1,2,3,4,5,6) would probably make the news. Has this ever happened in a major lottery? If yes, what was the public responce?
Double zero, let it ride
I'm wondering whether a randomized computation (Monte Carlo, etc.) has ever gotten a string of very unlucky random numbers, computed an erroneous result, and caused a real-world problem. [more inside]
Given an average rate how do I calculate how often to do something?
I get seed packets that (usually) give a germination rate. How do I calculate how many seeds to plant to give me a 'y' probability of getting 'z' seeds to germinate? [more inside]
2 problems of combinations and permutations.
How many unique ways are there to put X rocks into Y boxes?
(Given two different sets of attributes for both the rocks and the boxes.) [more inside]
Chance of event with small sample size, based on larger related sample?
Can/how can one improve the estimate for a chance of an event with a small historical sample size by utilizing the chance of a related event with a large historical sample size? Example and half-assed guess inside. [more inside]
The Gambler's Fallacy, of course. But maybe...
A coin flips three times and comes up heads 2/3. Not suspect.
But a coin flips 100,000 times and comes up heads 2 out of 3 times, that starts to look fishy. The standard probability of this is always roughly 50-50, but assuming a 2/3 ratio pointing to a "rigged" coin, how could you plot the increasing likelihood that a given coin is rigged? [more inside]
Bad at math
I have a question about probability math. I am essentially flipping a coin (except instead of a 50/50 chance, my odds are 50.5% heads, 49.5% tails).
I am concerned with the probability of me hitting heads (a 50.5% chance) several times in a row. [more inside]
Probability and a rather unique deck of cards.
Each card in a certain deck has three letters on it.
The first letter is either A, B, or C.
The second letter is either D, E, F, or G.
The third letter is either H, I, J, K, or L.
Every possible combination is represented exactly once in the deck. Ergo, there are 3x4x5=60 cards in the deck.
How can I determine the probability that a hand of X cards, drawn randomly from the deck, will include at least one of each of the letters?
Very specific probability question
Hi guys:
I hope that the green can help me on this- perhaps it's an easy problem for you:
I have 9 different playing cards and 2 players. The first player can take between 3 to 5 cards and the remainder are given to the second player, and then the game begins.
How many different starting hands (collectively between the two players) are there? The order of the cards in each player's hand does not matter. Thanks in advance!
I'm having trouble understanding likelihood ratios and diagnostic tests.
I'm struggling to understand likelihood ratios (LR) in the context of diagnostic tests, and why a positive LR is influenced by the sensitivity of the test. [more inside]
Is there a name for this logical fallacy? It has to do with statistics.
The fallacy is assuming that statistic information about a thing is more relevant in dealing with a particular instance of that thing than available first-hand data. [more inside]
What are the odds? Is intelligent design more plausible than chance?
I'm a cataloging librarian who works a couple hours a week on the reference desk. This morning I had a patron come in to ask me for sources that back up the claim that the probability that life on earth formed by random chance is so small that some kind of divine intervention is more likely. [more inside]
Human Random Generator
Can you think of a method that allows an individual to pseudo randomly create a sequence of numbers (at the very least the randomness is opaque to the minds of other people) assuming said individual may only use his mind and body (no physical tools are allowed)? [more inside]
What does a professional statistician do?
(Good) jobs involving probability and statistics other than math teacher or actuary? [more inside]
How to solve a complex statistics problem with a script?
In this game, you roll a number of six-sided dice to get a total. The total is either the highest single die result, or the sum of any multiples rolled, whichever is higher.
For example: If I roll three dice and get a 3, 4, and 6, my total is 6. But if I roll a 4, 4, and 6, my total is 8, the sum of the two 4s.
What I want to find out is the mean, median, mode, and standard deviation of the possible totals given N dice. How might I create a simple script to compute this? [more inside]
Practice Probability Word Problems
What great books or resources are there for practicing probability word problems such as for standardized tests like the GRE? [more inside]
Explain something easy to me.
What are the odds that two randomly selected people share the same bank PIN?
Statisticsfilter: Given available information about the distribution of self-selected 4-digit passwords (specifically banking PINs), is it possible to calculate the probability of two randomly selected individuals having the same PIN? If so, what're the odds? [more inside]
How do I calculate the probability of a specific sum of repeated die rolls?
I'm looking to learn how to calculate probabilities for a multi-round dice game. I've researched this question some, and it looks like I might need to know how to use the multinomial distribution, but I can't find any good introductions. Please point me to the most layman-accessible educational material on this subject, and help me to help myself. [more inside]
Gambling odds question
How would one (legally) take advantage of the change in odds of a given NFL team to win the Super Bowl? [more inside]
What are the odds?
Math/probability not sports: I am not a gambler, but I am trying out a method of betting on sports with some initial success. At what point can I use the numbers to confidently assume that this is down to the system rather than luck? [more inside]
A different fussy suitor from those I've met before
I'm working through an explanation/derivation of the secretary problem that I've never seen before. I know the eventual answer, and I understand most of the steps, but explain this to me like I'm an idiot: [more inside]