Probability (PRO), Spring 2022

Budapest Semesters in Mathematics

Péter Bálint
Office outside BSM: Egry József utca 1, Building H of the BME campus, office 509
Here is a map of the vicinity of building H
Text is: A First Course in Probability, by S. Ross


  • The syllabus, containing the topics covered, the course requirements, the detailed schedule (e.g., homework due dates). The content of the syllabus is continuously updated as more information becomes available, please check regularly. 
  • Lecture notes for the course, can be also regarded as a supplementary material to the Ross book.
  • Some material from my colleague András Vetier on height-weight joint distribution to demonstrate bivariate normals: height-weight  1. 2.
  • Here is an ad to demonstrate that probability is useful and interesting. (Not to mention the steadily increasing number of open positions in probability and applications in the industry.) Among others, we plan to cover the following questions:
    • What are the chances that there is no common birthday in a classroom?
    • The king comes from a family of two children. What is the probability that the other child is his sister? (Of course, not 1/2.)
    • The famous Monty Hall paradox (also featured in the series "Numbers"): Out of three doors, one hides treasure, two hide goats. You point to one of the doors, now Monty opens another door with a goat. Do you now think the treasure is behind your door, or behind the other one Monty did not open for you?
    • How certain should an inspector be when a new evidence occurs?
    • How worried should I be after a positive blood test for a serious, but rare disease?
    • Maybe Murphy was right? (Anything that can go wrong, will go wrong.)
    • If you have to rent an apartment within a month, and want to pick the best offer out there in the market, what is your optimal strategy?   
    • Where would you place the service stations for a bus route that travels between cities A and B?
    • Does a bus driver usually see more or less passengers than a passenger on the bus? Why?
    • What does it mean to be completely memoryless?
    • Would you rather fly a three-engine plane or a five-engine one?
    • How many chocolate chips should you plan per muffin so that less than 1% of customers get upset?
    • What are the chances that you can shoot a bullet out of the forest without hitting a tree?
    • How can we measure the value of π just by flipping a needle?
    • For how long will Jack and Jill wait for each other on a rendez-vous?
    • Eight students enter the elevator in a ten-storey building. How many times will the elevator stop?
    • How much time does it take for the lost miner to find his way out of the mine?
    • Upon receiving a noisy signal, what is your best guess for what has been sent?  
    • How many people should we ask when we make a survey?
  • The standard normal distribution in pdf.
  • Here you can find how a previous semester was taught.



If you have any questions, feel free to contact me (see above).