Questions tagged [probability]
A mathematical puzzle whose essential nature involves randomness. Use with [mathematics]
466 questions
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Alice and Carol's birthdates
Bob wants to guess Alice and Carol birth dates $b_{\text{Alice}}$ and $b_{\text{Carol}}$, they are both born on a common year. All dates contain a day and a month. We do not consider years.
At each ...
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Jane Street December 2025 Puzzle
It’s coming to the end of the year, which can only mean one thing: time for this year’s Robot Javelin finals! Whoa wait, you’ve never heard of Robot Javelin? Well then! Allow me to explain the rules:
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1 vs. 3 hide and seek challenge
There are four people playing hide and seek in a 1 vs. 3 format. Three of them are hiders, and the fourth is the seeker trying to find the hiders.
The game starts by the hiders choosing which zones to ...
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Irish pub gambling
Patrick is well known to visit Dublin's famous 'The Temple Bar Pub' daily since decades. He is systematically spotted to, kindly, challenge some pub customers to gamble.
Patrick has one fair die, and, ...
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Hiding the most helpful of three numbers
(This is a follow-up to Revealing the least helpful of three numbers.)
The game is like last time, but with one new step.
Andrew is secretly shown three real numbers, all independently, randomly, ...
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Sleeping Beauty's evaporating certainty
I thought of a little puzzle while contemplating the Sleeping Beauty problem.
The puzzle: create a variant of the Sleeping Beauty experiment (which involves one fair coin toss) where there is a ...
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What is the probability that at least one person draws their own name in randomized Secret Santa? [duplicate]
A group of 20 friends play "Secret Santa", and draw the name of their target randomly out of a hat.
What is the probability that at least one person draws their own name?
P.S.
Turned out to ...
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An odd question
On my way to and from work, there is a traffic light, where I wait anywhere between 0 and 1 minute. The waiting time is a random real number between 0 and 1 (independent and uniform).
Let x be my ...
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What is the probability that a random tetrahedron inside a sphere is intersected by the sphere's vertical axis? [closed]
A tetrahedron's vertices are independent uniformly random points in the interior of a sphere.
What is the probability that the tetrahedron is intersected by the sphere's vertical axis?
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Hat puzzle with rock, paper, scissors
Eight people are going to play a game where they work together to try to win a prize. They will all stand in a circle, and while their eyes are closed, a referee will place a hat on their head bearing ...
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What is the limiting probability that the polygon contains the circle?
A red circle is surrounded by a chain of n congruent green circles, with each green circle touching its two neighboring green circles and the red circle. On each green circle, a random (uniform and ...
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Which line is more likely to intersect the circle?
A green circle is tangent to a red circle and a black circle. The three circles have equal radii. Their centres are collinear and distinct.
Random point A is chosen on the red circle. Random points B ...
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A disk and a triangle: What is the probability of intersection?
An equilateral triangle has one vertex at the centre of a disk.
One side of the triangle lies completely outside the disk and is colored green.
A red line is drawn through two independent, uniformly ...
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Prime and Alphabet Draws - Puzzling Stack Exchange
The first prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, ...
At step one, you will draw 2 letters complety at random among the 26 letters of the alphabet.
You might for instance draw: "A&...
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Here is the probability, but what was the question?
While solving a problem about flipping coins, Blaise divided SPINED by STIPEND and got a probability of about 17.6%.
What problem was Blaise trying to solve?
(As usual in cryptarithms, the letters S, ...
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