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by henktijms
September 12th, 2018, 7:51 am
Forum: Book And Research Paper Forum
Topic: New Book- Surprises in Probability
Replies: 1
Views: 118

New Book- Surprises in Probability

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

https://www.crcpress.com/Surprises-in-P ... 0367000431
by henktijms
July 11th, 2018, 5:18 pm
Forum: Brainteaser Forum
Topic: How to choose your numbers?
Replies: 2
Views: 251

How to choose your numbers?

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...
by henktijms
November 3rd, 2017, 4:08 pm
Forum: Book And Research Paper Forum
Topic: New Book, Probability : A Lively Introduction by Henk Tijms
Replies: 3
Views: 803

Re: New Book, Probability : A Lively Introduction by Henk Tijms

Cuchulainn wrote:
gefeliciteerd!

Hartelijk dank!
by henktijms
November 3rd, 2017, 12:21 pm
Forum: Book And Research Paper Forum
Topic: New Book, Probability : A Lively Introduction by Henk Tijms
Replies: 3
Views: 803

New Book, Probability : A Lively Introduction by Henk Tijms

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...
by henktijms
April 30th, 2016, 10:21 am
Forum: Brainteaser Forum
Topic: Success runs with donuts
Replies: 1
Views: 1116

Success runs with donuts

<BR>There are 260 business days in a year. We have 54 employees. Each<BR>employee is required to bring donuts twice a year<BR>on different days. Each employee chooses the two days at random, independently of the other<BR>employees. What is the probability that there will be 10 business days in a row...
by henktijms
May 21st, 2014, 1:21 pm
Forum: Brainteaser Forum
Topic: Switch or SticK?
Replies: 7
Views: 5605

Switch or SticK?

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 , i...
by henktijms
May 20th, 2014, 4:29 pm
Forum: Brainteaser Forum
Topic: Switch or SticK?
Replies: 7
Views: 5605

Switch or SticK?

It is a brainteaser, not just a textbook exercise.
by henktijms
May 19th, 2014, 6:25 am
Forum: Brainteaser Forum
Topic: Devil's penny
Replies: 10
Views: 9234

Devil's penny

An interesting discussion on the problem and a variant of the problem can be found in

http://wordplay.blogs.nytimes.com/2014/03/03/devil/?_php=true&_type=blogs&_php=true&_type=blogs&_php=true&_type=blogs&_r=2
by henktijms
May 19th, 2014, 6:15 am
Forum: Brainteaser Forum
Topic: Switch or SticK?
Replies: 7
Views: 5605

Switch or SticK?

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. Next...
by henktijms
September 18th, 2013, 9:06 am
Forum: Brainteaser Forum
Topic: Devil's penny
Replies: 10
Views: 9234

Devil's penny

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 by...
by henktijms
September 18th, 2013, 7:42 am
Forum: Brainteaser Forum
Topic: Devil's penny
Replies: 10
Views: 9234

Devil's penny

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 bo...
by henktijms
April 27th, 2013, 9:24 am
Forum: Book And Research Paper Forum
Topic: Third edition of Understanding Probability book
Replies: 3
Views: 12124

Third edition of Understanding Probability book

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
by henktijms
April 8th, 2013, 9:33 am
Forum: Brainteaser Forum
Topic: Probability Question
Replies: 9
Views: 9931

Probability Question

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.
by henktijms
April 2nd, 2013, 5:10 pm
Forum: Brainteaser Forum
Topic: winning card game
Replies: 1
Views: 8469

winning card game

An interesting read (and money-maker)

http://www.youtube.com/watch?v=79SonkEK7c0

The win probabilities are surprisingly high. I guess they are found by Monte Carlo simulation rather than by solving numerically four-dimensional Markov chains with many thousands of states.
by henktijms
February 26th, 2013, 7:15 am
Forum: Brainteaser Forum
Topic: Good old die
Replies: 11
Views: 10114

Good old die

Wileysw, you give very clever counterexamples! The conditions I suggested for the underlying distribution of the loaded die are not strong enough to ensure that the induced Markov chain is aperiodic. Take your example with p_1=p_6=0.5 and r=5. Then the one-step transition matrix of the Markov chain ...