Questions tagged [probability]

A mathematical puzzle whose essential nature involves randomness. Use with [mathematics]

A probability puzzle is a puzzle, usually mathematical, that involves uncertain outcomes.

Probability puzzles often involve , , or , although other mechanisms may act as sources of uncertain outcomes.

For example: Left coin, right coin, last coin?

Another example of a probability puzzle is the Monty Hall problem: the game show problem with three doors, one car, and two goats.

General probability questions are off-topic but can be asked on our sister site Mathematics Stack Exchange with the tag (some questions can be found here).

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Monty Hall Revisited: Winning Both Goats!

Suppose you're at a game show, knowing the winning strategy for the classic Monty Hall problem. Your turn comes up and you take the stage. You confidently choose door number (?). Just as you are getting ready to tell the host you want to switch…
Tim
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A Strangely Familiar Probability Problem

You're taking the final exam for your Introduction to Probability and Statistics course, and once again you've failed to study (you were up all night solving online brainteasers). The exam is multiple choice. It asks 120 questions, each of which has…
COTO
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Shooting Free Throws

Shaq is shooting free throws. He makes his first shot, then misses his second. Confidence is a huge factor in how well Shaq plays. This means that for each subsequent shot, the probability he makes it is equal to the fraction of shots he has made…
Mike Earnest
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Contagious ants on a stick

Twenty-five ants are scattered on a meter stick. At the same time, they each pick a random direction (east or west) and start marching at 1cm/second. Whenever two ants meet, they turn around. When an ant reaches the end it falls off. The ant in the…
Mike Earnest
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Olivia's cookie jars

Olivia loves cookies so much that Dad promises to buy her two cookie jars on one condition: that she only eats one cookie per day. Olivia agrees, and now two black, large cookie jars rest on the kitchen table. The jars are completely opaque, but on…
Bogdan Alexandru
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Socks which may or may not match

You just won 2016 socks. Some of them are white, some are blue. The color of each sock was randomly chosen, with a 50/50 probability. Is it more probable that the socks can be paired, or that you will remain with two unmatching socks?
mau
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Expected Number of Tosses Until H,T,T,H

I found a nice little app/game the other day called Probability Puzzles. Apologies to those who, like me, will now obsess until they are all completed. I'm sure there will be many such people on this site! Anyway, Puzzle 14 of the Outrageous section…
Dr Xorile
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Asimov's Robot Balloon Trip

Chuck Asimov is a keen inventor and balloonist. He has developed some humanoid robots and decided to take nine of them (conveniently numbered 1 to 9) on a trip in his hot air balloon. Unfortunately the weather conditions have deteriorated rapidly…
Gordon K
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Probability that D wins this contest

Problem: $A, B, C, D$ are playing an archery game. They have equal probability of landing their arrow on any spot the target with radius of $R$. Their score is the distance to the center of the target. They take turn to shoot at the target $A, B,…
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Social Engineering (The Birthrate Problem)

The distant country of Toomalia has a birthrate of 67 boys for every 33 girls. In an effort to restore a 50:50 gender ratio in the country, Toomalian policymakers institute a mandatory new social policy: Couples seeking to have children may continue…
COTO
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Card probability problem

You have three cards in a hat. One is white on both sides, one is red on both sides, the third is white on one side and red on the other. You pull a card out of the hat and lay it down. The face is white. What are the chances that the other side…
BobRodes
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Two Dragons and a Princess

The Quest You are a knight tasked with rescuing the King's daughter. The princess is being held captive by a band of evil dragon pirate monks. You've been debriefed with prior intelligence gathered through reconnaissance to inform your journey. To…
WHY
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Coin with two heads

I was at a job interview and got a question. You have a bag with 100 coins. One of these coins has two heads, other coins are regular. You get one coin from this bag, put it on a table and see head. What the probability that this coin has two heads?…
glebmikh
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The Attack on Fort Alpha

I made this puzzle up in 1999 when I was a student. Fort Alpha, on your border territories, was attacked by The Enemy. You don't know if it fell, or repulsed The Enemy's vicious onslaught. A totally trusted advisor, with a detailed knowledge of the…
oggotron
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This Website Needs More Cat Pictures?

I love cats! And I love browsing cat pictures! :3 I stumbled on a webpage that shows random cat pictures every time I refresh the page. (For example, this site.) It has a database of $N$ cats and will pick any random picture in probability of…
athin
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