Riddle:  What is the probability that a dart, hitting a square board at random, lands nearer the center than an edge? Python Solution: Riddle source: https://www.cut-the-knot.org/Probability/ThrowingDarts.shtml

 Riddle: Three sticks of equal length are each uniformly randomly broken into two pieces.  What is the probability that from the three left pieces of the three sticks it is possible to form a triangle?  What is the probability that from the three longest pieces of the three sticks it is possible to form a triangle?  What is the probability that from the three shortest pieces of the three sticks it is possible to form a triangle?  What if the pieces are chosen randomly with the probability of 12 for each stick? Python Solution: Riddle source: https://www.cut-the-knot.org/triangle/ThreeBrokenSticks.shtml

 Riddle: 1. A moment of time is lucky if the hour, the minute and the second hands are in this order clockwise starting with the hour hand. A moment is unlucky if the order of the hands clockwise is hour, second, minute. Which is more probable?  2. A moment of time is lucky if the hour, the minute and the second hands all lie on the same side of some diameter of the clock face and unlucky otherwise. Which is more probable? Python Solution:  Riddle source: https://www.cut-the-knot.org/Probability/LuckyTimes.shtml

 Riddle: Take a wire stretched between two posts, and have a large number of birds land on it at random. Take a bucket of yellow paint, and for each bird, paint the interval from it to its closest neighbor. The question is: what proportion of the wire will be painted? More strictly: as the number of birds goes to infinity, what is the limit of the expected value of the proportion of painted wire, assuming a uniform probability distribution of birds on the wire?  Python Solution: Riddle Source: https://www.cut-the-knot.org/Curriculum/Probability/BOW1.shtml

 Riddle: 1. A point is dropped randomly on a unit segment. It divides the segment into two pieces. What is the average length of the shortest piece? The longest one? Their ratio? What is the expected value of the ratio of the lengths of the longest segment to the shortest one?  2. Two random points, chosen uniformly and independently on a unit segment, split the segment into three pieces. What is the average length of the left segment?  3. Two points are dropped randomly on a unit segment. They divide the segment into three pieces. What is the average length of the shortest piece? The longest one? Their ratio? Python Solution: Source: 1)  https://www.cut-the-knot.org/m/Probability/RandomPointsOnSegment.shtml 2)  https://mbapreponline.wordpress.com/wp-content/uploads/2013/07/fifty_challenging_problems_in__2.pdf

 Riddle: A man condemned to death in the State of Randomana is presented with the following probabilistic situation. He is given two similar bags, 10 white balls, and 10 black balls. He is asked to distribute the balls between the two bags as he wishes. Afterward, he will be blindfolded and allowed to randomly choose one of the bags. Then he will blindly draw one ball from the chosen bag. If he draws a black ball, he will be executed. However, if he draws a white ball, he will be pardoned. How should this unfortunate prisoner distribute the balls between the bags in the most favorable manner, namely, so that the probability of drawing a white ball at the end of the process is maximal? Python Solution: Riddle source: https://archive.org/details/understandingpro0000falk/page/48/mode/2up?q=2.3.9

Riddle: Two numbers x and y are uniformly distributed on [0, 1]. What is the probability that sides of length x, length y and length 1 form an obtuse triangle? Python Solution: Riddle source: https://www.cut-the-knot.org/Probability/ObtuseTriangleInSquare.shtml

 Riddle: Setzer throws a dart that lands within one of the 24 numbered regions on the dartboard shown, and then rolls a standard six-sided die. What is the probability that the number of the region his dart hits is the same as the number he rolls on the die? Express your answer as a common fraction. Python Solution: Riddle source: https://pvhsmathclub.weebly.com/uploads/1/2/1/3/121370108/2018_state_sprint_round.pdf

 Riddle: Two friends who take the metro to their jobs from the same station arrive to the station uniformly randomly between 7 and 7:20 in the morning. They are willing to wait for one another for 5 minutes, after which they take a train whether together or alone. What is the probability of their meeting at the station? Python Solution: Riddle source: https://www.cut-the-knot.org/Probability/GeometricProbabilities.shtml

 Riddle: Three points are randomly chosen on a circle. What is the probability that the triangle with vertices at the three points has the center of the circle in its interior? Python Solution: Riddle source: https://www.cut-the-knot.org/m/Probability/ThreeRandomPointsOnCircle.shtml

 Riddle: If three points are chosen at random, uniformly with respect to arc length, on the circumferences of a given circle, determine the probability that the triangle determined by the three points is acute. Python Solution:  Riddle source: https://cambomaths.wordpress.com/wp-content/uploads/2012/03/fivehundredmathematicalchallenges.pdf

 Riddle: What is the probability that three randomly drawn real numbers between 0 and 1 have a sum less than 1? Express your answer as a common fraction. Python Solution: Riddle source: https://pvhsmathclub.weebly.com/uploads/1/2/1/3/121370108/2018_state_sprint_round.pdf

 Riddle: It takes 5 minutes to cross a certain bridge and 1000 people cross it in a day of 12 hours, all times of day being equally likely. Find the probability that there will be nobody on the bridge at noon. Python Solution (still hesitant of the solution, correct me if wrong): Riddle source: https://cms.math.ca/publications/crux/issue/?volume=1&issue=10

 Riddle: Show that if two dice are loaded with the same probability distribution, the probability of doubles is always at least 1/6 Python Solution: Riddle source: https://seriouscomputerist.atariverse.com/media/pdf/book/Concrete%20Mathematics.pdf

 Riddle: A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed? Python Solution: Riddle source: https://artofproblemsolving.com/wiki/index.php/1996_AHSME_Problems/Problem_16

 Riddle: Three players in a team, each receives a hat (could either be red or blue). These are the rules of the game:  • The players act as a team. The team wins or loses, not individuals.  • When the hats have been placed on the heads there must be no communication between team members.  • All must answer simultaneously.  • Each is allowed to pass rather than guess a colour.  • The team wins if at least one player guesses correctly and none guess incorrectly. Otherwise, or if they all pass, it loses.  Note that it is perfectly permissible for the team to discuss a strategy before the placement of the hats; the question is, what strategy will maximize their chance of success? Python Solution: Riddle source: https://books.google.jo/books?id=a1EUZ5qZkm8C&printsec=copyright&redir_esc=y#v=onepage&q&f=false

 Riddle: The probability that the square of a positive integer (in decimal notation) ends with the digit 1 is 2/10 because out of every 10 numbers those and only those ending with the digits 1 or 9 have squares ending with 1. What is the probability that the cube of a positive integer chosen at random ends with the digits 11? Python Solution: Riddle source: https://www.scribd.com/document/63961838/A-Friendly-Mathematics-Competition-35-Years-of-Teamwork-in-Indiana

 Riddle: What is the probability that a power of 2 begins with the digit 1? Python Solution: Source: https://archive.org/details/ChallengingMathematicalProblemsWithElementarySolutionsVol1DoverYaglomYaglom/mode/2up?q=What+is+the+probability+that+a+power+of+2+begins+with+the+digit

 Riddle: Teams A and B plays a series of games, each with three possible outcomes: A wins, B wins, or they tie. The probability that A wins is p, the probability that B wins is q, they tie with the probability r =1-p- 4. The series ends when one team has won two more games than the other, that team being declared the winner of the series. What is the probability that team A wins the series? Python Solution: Riddle source: https://www.cut-the-knot.org/Probability/InPraiseOfOdds.shtml

 Riddle: An ordered pair ( b , c ) of integers, each of which has absolute value less than or equal to five, is chosen at random, with each such ordered pair having an equal likelihood of being chosen. What is the probability that the equation x^ 2 + bx + c = 0 will not have distinct positive real roots? Python Solution: Riddle source: https://artofproblemsolving.com/wiki/index.php/1979_AHSME_Problems/Problem_27