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2. Buffon's needle problem - Wikipedia

   en.wikipedia.org/wiki/Buffon's_needle_problem

   Similar to the examples described above, we consider x, y, φ to be independent uniform random variables over the ranges 0 ≤ x ≤ a, 0 ≤ y ≤ b, − ⁠ π / 2 ⁠ ≤ φ ≤ ⁠ π / 2 ⁠. To solve such a problem, we first compute the probability that the needle crosses no lines, and then we take its complement.

3. Boy or girl paradox - Wikipedia

   en.wikipedia.org/wiki/Boy_or_Girl_paradox

   The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, [1] Mr. Smith's Children [2] and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner featured it in his October 1959 " Mathematical Games column " in Scientific ...

4. Bertrand's box paradox - Wikipedia

   en.wikipedia.org/wiki/Bertrand's_box_paradox

   A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be ⁠ 1 / 2 ⁠, but the probability is actually ⁠ 2 / 3 ⁠. [1] Bertrand showed that if ⁠ 1 / 2 ⁠ were correct, it would result in a contradiction, so ⁠ 1 / 2 ...

5. 100 prisoners problem - Wikipedia

   en.wikipedia.org/wiki/100_prisoners_problem

   In the following years, the problem entered the mathematical literature, where it was shaped in further different ways, for example with cards on a table [6] or wallets in lockers (locker puzzle). [2] In the form of a prisoner problem it was posed in 2006 by Christoph Pöppe in the journal Spektrum der Wissenschaft and by Peter Winkler in the ...

6. Monty Hall problem - Wikipedia

   en.wikipedia.org/wiki/Monty_Hall_problem

   As already remarked, most sources in the topic of probability, including many introductory probability textbooks, solve the problem by showing the conditional probabilities that the car is behind door 1 and door 2 are ⁠ 1 / 3 ⁠ and ⁠ 2 / 3 ⁠ (not ⁠ 1 / 2 ⁠ and ⁠ 1 / 2 ⁠) given that the contestant initially picks door 1 and the ...

7. Coupon collector's problem - Wikipedia

   en.wikipedia.org/wiki/Coupon_collector's_problem

   In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...