r/probabilitytheory

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I’ve been building a project called MeetProba for students preparing for quant interviews.

The idea came from a frustration I had while preparing myself: probability resources are often either too theoretical, poorly structured, or not really aligned with what gets asked in quantitative finance interviews.

And even when you find good exercises, the solutions are often not detailed enough or skip important reasoning steps.

So I started building a platform specifically focused on:

• combinatorics
• random variables
• stochastic processes
• Markov chains
• Brownian motion
• and other probability topics commonly used in quant interviews

The main idea is to make preparation more structured and interview-oriented through:

• carefully selected exercises
• detailed step-by-step solutions
• roadmap/dependency graphs inspired by NeetCode
• progression between topics

The platform is currently free to use.

I attached a few screenshots of the current version and would genuinely love feedback from people preparing for quant roles or probability-heavy interviews.

https://meetproba.com

Hi everyone !

I'm interested in calculating this probability: I'd like to calculate the probability of obtaining, by encrypting a coherent sentence, another coherent sentence (taking into account the possibility of obtaining a sentence in a different language). This is similar to a possible application of the Library of Babel, where all the books that have ever existed and will ever exist can be found in this library. However, in my case, I'm working with data encryption such as the Caesar code.

I'm not sure how to calculate this probability so any help would be welcomed. Thank you in advance.

take the infinite monkey theorem for example. after an infinite amount of time, will an infinite amount of monkeys NOT type shakespeare? or does it technically HAVE to happen simply because it’s infinity? it’s almost like a paradox of sorts, with infinity, everything must happen, which also includes everything not happening. i’ve barely graduated from school and dont know too much regarding theoretical probability, i just like to think. hopefully what im saying makes sense, id be interested to hear what you guys have to say!

So basically i added a guy on insta. He had a gym pfp and i was like “i f with that” . Then i posted a gym story and he replied asking questions abt gym and stuff. We had a small convo and he said icl ur cute why dont we go for a gym session. So i agreed cz lowkey i was like why not atleast we share same interests maybe we can be friends or i will find out.

Tbh i didnt have expectations or anything in my head its just ill have some fun time. So then he suggested like why dont we just go somewhere before gym. So i agreed cz why not. So after that we had good deep convos . Tbh i was enjoying it but not in a romantic way or like i wanted him. Its more that i finally found someone to share my thoughts with.

So he kept giving me eye contact, lowkey i wasn’t attracted like i didn’t like his looks, and i didn’t feel the vibe i was repulsed. Then the next day we also went out. He started talking abt relationships and out of nowhere he was like “ how many times u gave a head” i said im not comfortable answering it and i wanna keep it private .

So then i wanted to pay for myself cz tbh im not interested like i like him but not in way that i want to be in a relationship. So i told him mid convo that i dont want to be in a relationship ( i was generally speaking obv)
So then he acted normal. Went to the gym he became abit weird . I also acted weird like i was dissociating and i felt numb like i couldn’t think or talk or anything . So i started being sarcastic 99% of the time and i was jk i was like my name isn’t(_) its that (_) and because i was saying it so casually and i was numb he believed it and he became very uncomfortable and he was like wdym
I was like im being sarcastic. And he was just concerned i can see it in his eyes cz he doesn’t know if most stuff was sarcastic or not.

Then i asked him for help with the machine i said “ can u help me my guy” he said “ dont ever say my guy” i was like wdym he said “ im not ur guy” i was like “ my friend “ he was like im not ur friend i was like what do u want me to say . He said nth just ask for the help already.

And this guy had some beliefs abt women should do this and that men should do that blah blah. I dont like this shi. Im more like a 50 50 person.

But yh after this we just snap but nth to serious and he still asked me to go out again. Then he reposts stuff abt him not believing woman and men can be friends.

So like do u think im weird? Or do u advise

This problem occurred to me, I reached an impasse. I'm sure it's easy to someone with an actual background in probability (I just took an introductory course). Not homework, just fun.

Problem:

A person lives on the x axis. They start at the origin. They repeatedly throw a coin. With probability p, they move by 1 to the right, and with probability 1-p (denote q), they move by 1 to the left (0<p<1).

Let n be a positive integer. What is the expectation of the number of steps until they are at position n? Is the answer that the expectation is unbounded, since they could just keep drifting leftward? If so, what if we ask what is the expectation of the number of steps until the reach either position n or position -n?

My first attempt:

For any position x, denote the expected number of steps until we reach position +n by E(x)

My first observation is that for any distance k from position n, with probability 0.5^k your next k steps are rightwards, and you reach position n. The contribution to the estimate is k*0.5^k. I tried to generalize this: The contribution of any path involving a steps left and k+a steps right is the probability of any specific such path, (q^a * p^(k+a)), times the number of such paths, ((k+2a) choose a), times the expected number of steps (k+2a).

Thus, if we assume that with probability converging to 1 we will always eventually reach +n**,** then the expected number of steps is

Sum (over a=0,...,infinity) of [(k+2a) * (q^a * p^(k+a)) * ((k+2a) choose a)]

= k + 2 * Sum (over a=0,...,infinity) of [a * (q^a * p^(k+a)) * ((k+2a)* choose *a)]

At which point I'm stuck.

-----------------------------------------

My second attempt:

Next approach, a recurrence relation: for any position x, denoting the expected number of steps until we reach position +n by E(x), then so long as x<n:

E(x) = p(1 + E(x+1)) + (1-p)*(1+ E(x-1)) = 1 + pE(x+1) + (1-p)E(x-1)

Obviously (I think?) E(n) = 0

OK, so here was my thought: re-arrange the recurrence relation so that it keeps expanding rightwards, until we reach n. Except I hit a snag. But let's try. Denote q=1-p:

E(x)=1 + pE(x+1) + qE(x-1) ;; move pE(x+1) to the left-side.

E(x) - pE(x+1) - 1 = qE(x-1) ;; , divide by q

E(x-1) = E(x)/q - (p/q)E(x+1) - 1/q

Increase the index on both sides by 1 (implicit assumption: x<n-1):

E(x) = E(x+1)/q - (p/q)E(x+2) - 1/q

At this point, for simplicity, I set p=q=0.5. So

E(x) = 2E(x+1) - E(x+2) - 2

==>

E(0)=2E(1)-E(2)-2

= 2 [2E(2)-E(3)-2] -E(2) -2 = 3E(2)-2E(3) -4 - 2

= 3[2E(3)-E(4)-2] -2E(3) - 4 - 2 = 4E(3) -3E(4) - 6 - 4 - 2

At this point I realized a problem: I'll always have two expectation values. But I only know E(n)=0, and no other E(k). Thus, an impasse.

Several years ago I drove for FedEx. Was in Harvard Square, Cambridge MA sitting in traffic when saw Dad, Mom and teenage girl walking past me. Daughter had very unusual shirt on (basically no back, just straps). Saw them like 5 times before made it thru the square. 5 hours later, I am on the other side of Cambridge, about 5 miles or so, when I see the same family walking.

How do you calculate the odds/probability/chances (don’t even know what to call it) that 1, I saw them in the first place (would it be 7 billion to 1? Or, just like 1000 to 1, the number of people in Harvard Square at the time?) and 2 that I saw them again hours and miles later? I mean, if I had been +/- 5 minutes I would have missed them both times. Don’t even know how to begin to figure it out. TY in advance!