Fun material are the tutorials Kuhn-Tucker Conditions, Gambling and Investing and Markov Chains, Roulette and Google Search . The tutorials were specially written for the online magazine Sector of the econometric and operations research students in Amsterdam and can be downloaded from https://www.kr...

Fun read: Surprises in Probability, Seventeen Short Stories by Henk Tijms

https://www.crcpress.com/Surprises-in-P ... 0367000431

On each of 100 blank cards you have to put one of the numbers 1, 2, 3, 4 or 5. If this has been done, one of the cards is randomly drawn.You have to pay in dollars the same amount as the number on the card drawn. How to put  your numbers on the cards in order to minimize the  maximum  of  $E(X_1)\ld...

gefeliciteerd!

Hartelijk dank!

Hello everybody, my new book has just come out Paperback: 535 pages Publisher: Cambridge University Press ISBN 978-1-108-40784-7 The book covers all of the standard material in introductory probability, but it deals also with many other topics that are usually not found in other books- such as  Kell...

<t>There are 260 business days in a year. We have 54 employees. Eachemployee is required to bring donuts twice a yearon different days. Each employee chooses the two days at random, independently of the otheremployees. What is the probability that there will be 10 business days in a row where nobody...

<t>Vanubis1, the criterion is to maximize the probability of getting the $100 bill and not to maximize the expected dollar value of the third bill. By the way, I think the expected dollar value when switching should be (1/3)*100*P(A\C)+1.4*P(B\C) rather than 100*p(A/C)+1.5*p(B/C) . As I said before ...

It is a brainteaser, not just a textbook exercise.

An interesting discussion on the problem and a variant of the problem can be found inhttp://wordplay.blogs.nytimes.com/2014/03/03/devil/?_php=true&_type=blogs&_php=true&_type=blogs&_php=true&_type=blogs&_r=2

<t>Two boxes are placed in front of you. One box contains nine \$1 bills and one \$5 bill, while the other box contains two \$1 bills and one \$100 bill. You choose at random one of the two boxes and two randomly picked bills are taken out of the box. It appears that these two bills are \$1 bills. N...

<t>The amounts a_1, ... ,a_10 are given amounts. As an example a_i=i as in: A game is played with eleven cards: an ace, two, three, $\ldots$, nine, ten, and a joker. These cards are thoroughly shuffled and laid face down. You can flip over as many cards as you wish, but they must be flipped over one...

<t>You play the following game. Eleven closed boxes are put in random order in front of you. The boxes $1,\ldots, 10$ contain $a_1,\ldots, a_{10}$ dollars, but box 11 contains a devil's penny. You may open as many boxes as you wish, but they must be opened one by one. You can keep the money from the...

As additional supplement, more than 150 probability exam questions with fully worked-out solutions can be downloaded from http://personal.vu.nl/h.c.tijms/ExamQuestionsUP.pdf

Vanubis1, how did you analytically solve this problem? The only analytical solution method I see is using a recursion for a five-dimensional Markov chain.

<r>An interesting read (and money-maker)<YOUTUBE id="79SonkEK7c0The" url="http://www.youtube.com/watch?v=79SonkEK7c0The"><URL url="http://www.youtube.com/watch?v=79SonkEK7c0The">http://www.youtube.com/watch?v=79SonkEK7c0The</URL></YOUTUBE> win probabilities are surprisingly high. I guess they are fo...