Fifty Challenging Problems in Probability with Solutions

by Frederick Mosteller

Remarkable selection of puzzlers, graded in difficulty, that illustrate both elementary and advanced aspects of probability. Selected for originality, general interest, or because they demonstrate valuable techniques, the problems are ideal as a supplement to courses in probability or statistics, or as stimulating recreation for the mathematically minded. Detailed solutions. Illustrated.

Genres: Mathematics, Puzzles, Science, Finance, Textbooks, Nonfiction, Physics

96 pages, Paperback

First published January 1, 1965

Reviews

[Bart Van Loon]

15 years after ending my computer science and mathematical studies, I thought it was time for me to try out this little booklet. I think I made a good start, but soon enough the challenges became too hard for me to solve unguided. :-) Still, it served as a good reminder that statistics are not at all intuitive, which is especially useful to know in this day and age of big data (and COVID-19 related statistics all over the news).

The solutions were always clear enough however and the collection had no problem whatsoever keeping my interest level high. The reason I'm not 100% sure this publication deserves more stars is that, even though maths never gets old, the problems used to frame the maths do feel quite out of place in the 21st century.

[Tristan]

Mostly straight-forward questions. Some solutions are merely discussions instead of rigorous proofs. Concluding problems are, let's just say, a bitch.

[Gautam Gopal Krishnan]

This is a fun book of puzzles and riddles that are actually problems in probability. While the title is Fifty Challenging Problems in Probability with Solutions, there are fifty six problems which the author concedes in the preface to the book. Given that the book was originally published in 1965, the brain teasers feel timeless and it is encouraging to find complete solutions (and discussions) printed at the end of the book. The one place where the book feels old is when Fermat's last theorem in the form of Molina's urns is stated as unsolved while it has been solved (in 1995).

One can enjoy this work with elementary understanding of probability and combinatorics. The problems are helpfully grouped together where it makes sense. While not all problems might be challenging, there are some truly involved questions and a handful of open ended questions that are exciting to ponder upon. This is a nice refresher for people wanting to think about mathematically inclined riddles as the material captures the zeitgeist of probabilistic puzzles.

[Robert]

This was another book I purchased the summer I decided to teach an AP statistics course. I studied quite a bit. This book was interesting. Several interesting puzzles were presented. Then the math behind the puzzles was explored. It's an interesting enough read.

[Rejeev Divakaran]

Very interesting problems. Though not very challenging. Good brain teasers.

[mirela Darau]

The problems treated are somewhat classic for the sort of book, but the idea is nice,and many of them can be approached in a sufficiently intuitive manner. I like it, and found it useful in teaching.

[Jessada Karnjana]

มีโจทย์ท้าทายทั้งหมด 56 ข้อ ครอบคลุมทุกระดับทั้งง่ายและยาก มีปัญหาคลาสสิกหลายปัญหา Bridge, Craps (เกมพนันยอดฮิตเกมหนึ่งของอเมริกา), prisoner's dilemma (ที่พบเป็นตัวอย่างฮิตในทฤษฎีเกม), ปัญหาสะสมคูปอง, ปัญหาลูกเต๋าของ Pepys ที่เขียนจดหมายปรึกษานิวตัน, ปัญหาการเดินสุ่ม 2 มิติ 3 มิติ, เข็มของ Buffon, trick ที่ทำให้เหรียญมีโอกาสออกหัวไม่เท่ากับก้อย ฯลฯ ปัญหาเล่มนี้สนุกทุกข้อและหลายข้อมีคำตอบชวนประหลาดใจ อ่านได้ตั้งแต่ระดับมัธยมถึงอุดมศึกษา คนทั่วไปที่มีความรู้ความน่าจะเป็น ม.ปลายสามารถสนุกกันมันได้

[shishir]

This book has well-known puzzles, but the solutions are excellent. Great for problem solvers, even if the puzzles are familiar.

Many of the puzzles featured in the book are well-known and considered common knowledge among enthusiasts. Since I had previously encountered these puzzles in various forms, I was hoping for a more extensive selection, perhaps leaning towards Olympiad-level complexity.

[David Khosid]

Great set of problems in probability for math nerds in a very thin book. But don't let its size fool you, it has a high signal-to-noise ratio. Each problem is thought-provoking and often leads to interesting generalizations. I enjoyed solving the problems, and going through the provided solutions.
I'd love to have more books like this one!

[Vishal]

The problems start off easy and then gradually become more challenging. The content strikes a good balance between real-world applications and math-focused material. The font size was too small going from the TTM series.

[Kate]

Interesting problems and clear explanations. The author tried to group similar problems with variants together.

[Keshav]

Overrated: not challenging enough and it's quite annoying since it's right there in it's name

[Tazik Shahjahan]

WIP: 15/50

[Zhang Chenxi]

interview prep

[Vincent]

Reading this to prepare for a Quant interview.
Wish me luck.
PS: I did not get the internship, but it was still an enjoyable read.

[Данило Судин]

Цікава книжка, першу половину задач з якої мені вдалося (відносно) самостійно розв’язати. От з другою половиною не склалося, бо слід вміти диференціювати та інтегрувати, а також додавати безконечні числові ряди, тобто знати вищу математику.

Втім, з книжки я все ж "виніс" одну цінну ідею: зрозумів сенс формули гіпергеометричного розподілу. А це добре, бо тепер відмінності між відбором з поверненням та без повернення у вибіркових дослідженнях можу описати математично.

[Scott]

Most of the examples are easily found on the internet or in standard probability textbooks, so purchasing the book itself isn't all that useful.

[Lisa]

The problems were quite basic, but interesting. I use mathematics almost daily, so the problems were a bit too simple. However, my grandfather really enjoyed them.

[Rajesh Kumar]

wanna read this book

[Jimmacc]

Great book to challenge yourself