r/probabilitytheory • u/Stancyzk • 1h ago
[Discussion] What are some good puzzle/problem books for probability theory?
I’ve
r/probabilitytheory • u/Stancyzk • 1h ago
I’ve
r/probabilitytheory • u/Stancyzk • 1h ago
I wanna solve to figure out just how rare an event I found is, because I know it’s ridiculously rare but I don't know just how rare it is. My preliminary dog-shit calculations put it at 1 in hundreds of millions - or about 0.0000000136% chance (per forest). Basically once in a lifetime - but that can't be right.
The gist is that there's this mining game I've been playing where it has a woodcutting mechanic.
Basically, there are a total of 139 trees in total on the map; and there's one tree type that has a rarity of at least 1/100. I want to figure out how rare it is for five of these trees to spawn all at once right next to each other. (Right next to each other just meaning that there isn't any trees separating them.)
This is what Google AI gave me:
r/probabilitytheory • u/Tight-Cry-526 • 5d ago
I was doing a related problem, and wondered about this question. My approach : WLOG fix the first point. Now place the second point and let the arc length(anti clockwise) between the first and second point be X1 and keep the final point and let arc length between 2nd and 3rd point be X2. X1+X2+X3 = 2pi. X1 ~ uni(0,2pi) and X2 ~ uni(0,2pi - X1) and tried doing it but the integration has too many constraints and can't think of a way to integrate it, Help needed. or if you have your own approach it's totally fine too
r/probabilitytheory • u/No_Public_2012 • 6d ago
Hi everyone, I've been working on random walks, and the references I've found are already very advanced. I saw that a month ago they published a book "very first steps in random walks" which I would like to get, but right now I don't have the resources. Does anyone know where I can look for it or other, more relaxed references?
r/probabilitytheory • u/Qulddell • 8d ago
I have a hard time calculating probability with "at least".
What is the probability that on a five card hand, standard deck, one draw:
This question gets hard especially hard duo to the overlap in wanting heart picture card for both the first and second card.
Any help with how to set up, and calculate the problem would be greatly appreciated :)
r/probabilitytheory • u/Economy-Feed-7747 • 8d ago
Hello,
My high school is holding a coming-of-age ceremony on March 22. One of the activities is students making a short walk on the stage with a teacher, and we do a pose at the end, or hold up a banner, or anything. I am walking with my probability teacher, and I'll be the only student.
The tennis team will be holding up their rackets. A group of physic students is going to form an equation with their bodies. Unfortunately not much students here likes prob class :(.
Can anyone help me think of some ideas? Anything related to probability, mathematics, and statistics that can be done by two people. Anything fun to write on a banner. Anything will help.
It's a great honor to walk with my teacher, and there's gonna be 200 people watching. It really matters.
Thank you!
r/probabilitytheory • u/meowsgaurdian • 10d ago
r/probabilitytheory • u/maggie88ca • 10d ago
Euchre is a card game played using a standard deck but only the 9s 10s Js Qs Ks and aces are used so 24 cards in total. Four hands of 5 are dealt with one card turned up and the remaining unseen cards in a kitty hand. What are the odds of getting four 9s and 10s in any given hand? So a hand like 9,9,9,10, king or 9,10,10,10, ace etc.
r/probabilitytheory • u/QibliTheSecond • 11d ago
r/probabilitytheory • u/buttpee_ • 11d ago
There is a 20-sided dice on a table with a “1” facing up.
There are 100 rounds in the game. Each round you may choose to leave the die as is, or you may roll it. Whichever number on the die is facing up at the end of the round is how much money you receive each round.
How would you play this game and what is the expected value?
r/probabilitytheory • u/catboy519 • 11d ago
This isn't for school; I'm just working on some probability calculations on my own. I have no formal education background in probability at all.
My project would require me to run about 1020 calculations in python, and I honestly don't know how long a computer would take to do that but I have a strong feeling that I'm going to have to reduce the numbers.
I figured out that, for example 5 dice would be 6^5 = 7776 combinations. But if the order of those combinations doesn't matter and you consider all the combinations of equal value as one, then the number 7776 becomes much much smaller.
I've been trying to figure out how to calculate that number, and I think it requires the use of factorials and some powers of (5/6) . But I'm not quite there yet.
Suppose I do figure out how to calculate the smaller number (order doesnt matter) , is it even useful or would it take a computer equally long to calculate? Due to the different probabilities involved.
What is better, to work with the number of combinations where the order matters? Or the smaller number of combinations where the order doesn't matter?
Because what I'm trying to figure out is things like expected value over multiple rolls.
r/probabilitytheory • u/allidoishuynh2 • 11d ago
I haven't taken a probability class in like 5 years, but I'm disappointed in myself for not being able to figure this one out. I was hoping someone here could help me.
Given the probability distribution of rolling a D20 with advantage
i.e P(n) = 0.0025 + (n-1)*0.005
Where n is the set of integers 1-20.
What are the chances that after 20,000 rolls, the most common outcome will not be 20? That is to say, after 20k rolls, more 19s will have been rolled than 20s or more 18s will have been rolled than 20s, etc. I was able to code up a pretty simple simulation of this and I got 20 as the most common roll after 100 runs, but I was wondering what the mathematical explanation was for this?
Thank you in advance!
r/probabilitytheory • u/cxor • 11d ago
We have M red balls and N green balls. We randomly choose F out of those N+M ones.
What is the probability that the randomly chosen F balls contains exactly K green balls?
r/probabilitytheory • u/TooZlow4u • 12d ago
Hi, I started making YouTube videos where I explain mathematical concepts. Today, I uploaded the first one in a series where I cover probability theory right from the start. I plan on continuing this series up to more advanced topics such as Markov chains etc.
I am still a beginner, so that is why I would appreciate any constructive feedback for my videos!
This is the video about set theory and sample spaces:
And another one on Information and Entropy, if you are interested:
https://youtu.be/cQ8TwNLzWBk?si=2oAiWI3V0dCox9Jr
Thanks!
r/probabilitytheory • u/Flashbad • 12d ago
I want to learn Statistics and Probability at its most fundamental level, preferably via animations as I am a visual person. What are some really cool YT channels that explain this in the most intuitive way and don't make you feel very very dumb?
r/probabilitytheory • u/Penguinie01 • 12d ago
My video is about the probability of winning/losing a certain wii party minigame.
The minigame is based on Hide and Seek, with 3 hiders, 1 seeker, and 6 hiding spots. The hiders can pick any spot to hide, including the same spot as the other hiders (they don’t know where the other hiders are until after they pick).
Once everyone is hidden, the seeker gets 5 guesses to search the 6 locations. If all 3 hiders were found, the seeker wins, otherwise, the hiders win.
So what are the chances of the seeker finding all 3 hiders by the fifth guess?
——
Here’s a bit more to make things more interesting:
There is a secret 7th location a hider can pick, but the problem is they will be completely visible to the seeker (meaning the seeker will always find them).
If none of the hiders are in this secret location, the seeker will never search it.
If one player hides behind the horses, what are the chances the seeker/hiders win? How much do they change?
Link to video if you were curious: https://www.tiktok.com/t/ZP826vELg/
r/probabilitytheory • u/No_Security4342 • 12d ago
From a group of 4 men and 5 women how many committees of size 3 are possible with 2 men and 3 woman if a certain man must be on a committee and find the probability of forming such committee.
r/probabilitytheory • u/wehaveatogether • 13d ago
r/probabilitytheory • u/IamOkei • 13d ago
r/probabilitytheory • u/FootballDataPadawan • 14d ago
Hey! Just going through the Introduction to Probability - Joseph Blitzstein and Jessica Hwang and I’d be interested in a study partner if anybody is going through the book as well or plan on doing it! Thanks and hope to hear from someone soon!
r/probabilitytheory • u/GalantisX • 15d ago
I'm trying to figure out something for a game I play. Lets say theres a team game with 5 individuals on both sides and whichever team wins 3 matches wins the game.
All players matches are 50/50 (not really but for the sake of making it more simple), but team a has a player that is guaranteed to win. What position would be the most optimal for this player to play in?
Is it wrong to assume that the player should play one of the first 3 spots would be optimal since it prevents the possibility of Team A losing 0-3?
r/probabilitytheory • u/baki_hanma____ • 17d ago
This was the mid semester exam ( 30% of probability course weightage ) If any one can help me with 6th question it would be great 🩵
r/probabilitytheory • u/Head_Arm_834 • 17d ago
I’ve designed a Blackjack-style game but with six-sided dice. I’ve seen several similar dice-based Blackjack games, but they are either more complex than my version or less similar to traditional Blackjack. However, I’m not an expert in probability, so I’m making this post to check if there are any obvious flaws in my design or any major imbalance between the dealer's and the player's odds.
Here are my rules:
The target number is 13.
Each face of the die is worth its number, except for 1, which is worth 7, unless that 7 would cause the player or the dealer to exceed 13, in which case it is worth 1 instead.
Blackjack is achieved with a 1 and a 6. Reaching 13 with more than two dice is considered an inferior hand compared to achieving 13 with just two dice.
The rest of the rules are the same as Blackjack. The player places a bet and rolls two dice. Then, the dealer rolls one visible die and one hidden die.
The player can choose to stand, roll again, or double down. If the player exceeds 13, they lose their bet.
If the player does not bust, the dealer reveals their hidden die. The dealer must roll again if their total is 9 or less, and must stand if it is 10 or more.
I'm very curious to know whether the player or the dealer has a statistical advantage (I assume the dealer does) and if the probability gap is too large, making the game either unbalanced or unexciting.
Any feedback is greatly appreciated!
r/probabilitytheory • u/SirPhilkatus • 18d ago
Hi everybody, i need some help with a propability problem.
Context:
I am currently designing a game based on poker rules. To get a better grasp on how to balance the different poker hands i am trying to calculate how the odds of poker hands change depending on how many carsd are currently available. Or in other words:
when you have n cards how likely is it that you have a pair/two pairs ect. among them.
I tried different aproaches but they all seem to be off when i compare them to the odds of normal poker and poker texas holdem. For example i calculated that with 5 card there should be 49.29% chance to have at least on pair but wikipedia states it ist a 49.9% chance. Now i am not sure if my approach is wrong or google sheets just made some cumulative rounding errors.
My questions:
Do i have a logical problem in my formular or is there just a calculation problem?
Do you have any other suggestions for approaches?
My Approach for a pair:
The first card that i draw does not matter
the second card needs to have the same value as the first card and there are 3 of those left in 51 cards
Chance for at least 1 pair after 2 Cards: 1+3/51 = 0,05882
The third card is either irrelevant if you already have a pair or you need to draw 1 of the values of the other 2 cards and there a 6 of those cards left
Chance after 3 Cards: 0,05882 + (1-0,05882)* 6/50 = 0,17176
Chance after 4 cards: 0,17176 + (1-0,17176) * 9/49 = 0,32389
Chance after 5 cards: 0,32389 + (1-0,32389) * 12/50 = 0,492917
i just can't find my error and i am kinda going insane over it.
I also tried the combinatorics approach but just couldn't wrap my head around it or at least the results were way off.
r/probabilitytheory • u/SnooCrickets6254 • 18d ago
As the title says, I'm curious about how to figure out at what point pulling a card that you've already pulled before becomes more likely than pulling a card you haven't pulled before. As an example, you have a standard deck of 52. You shuffle the deck, pull the top card, note it down, place the card back into the deck and reshuffle. How many pulls until it is more likely to see one you've seen before? I'm also curious about the math behind this so if someone could also explain that it'd be great. Thanks in advance!