Questions tagged [probability]
A mathematical puzzle whose essential nature involves randomness.
322
questions
1
vote
3answers
148 views
Random sum adds to 1000 [closed]
A random whole number is generated between 1 and 1000 inclusive, and added to a sum. A new randomly generated whole number is generated and added to the sum until the total sum is greater than or ...
6
votes
5answers
1k views
Probability of three identical digits on a four-digit digital clock?
On a digital clock showing 00:00 to 23:59, what is the probability of having exactly three identical digits?
5
votes
4answers
329 views
A probably sunny Sunday
Besides this problem I also use the following one to rise the interest of my students on the Probabilities Theory. It's a funny puzzle were the use of simple arithmetic rules doesn't work. We have to ...
7
votes
2answers
209 views
Searching for the Covid vaccine
You have 1000 possible Covid vaccine candidates. You need to test them and find out if one works as quickly as possible. The test is to apply a small drop of a vaccine candidate to a sample, and ...
8
votes
1answer
105 views
Black-hat/white-hat logicians with a bell and a meal
At the 2020 yearly black- and white- hatted logician gathering, the following fun activity is organized.
$N$ logicians will sit around a table, each wearing a black or a white hat the color of which ...
10
votes
1answer
465 views
Mathematics in adolescence
When I start to teach probabilities, I challenge my students with the following:
Thelma is 16 years old and can only go out at night if one of her parents gives her permission. She knows her father ...
1
vote
0answers
60 views
Choose the single correct answer [duplicate]
If you choose an answer to this question at random, what is the chance that you will be correct?
A. 25%
B. 0%
C. 50%
D. 25%
3
votes
2answers
130 views
Broken stick riddle
There is a famous mathematical riddle called The Broken Stick Problem. Here’s the extension:
If a straight stick is accidentally broken into three pieces, the probability of being able to form a ...
8
votes
4answers
519 views
Circle inside circle
Here's a fun little math problem I made(by fun I mean no complicated methods needed at all.)
You have a large circle with radius N with a cross in it to seperate the 4 quadrants(so that the figure ...
6
votes
2answers
784 views
Exam statistics
250 teenagers gather for an exam. Peeking at the roll, a math-inclined among them note that if they are split into 10 groups of 25 per alphabetical order, then in each group, there are two with the ...
10
votes
3answers
260 views
Find a good strategy to survive the multiplayer duel
Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
10
votes
3answers
3k views
Lottery strategy
In a city, the official lottery consists of scratch cards that cost 10 bucks each. Each scratch card contains 36 squares with a hidden number on each square : 21 of them are “zeroes”, 9 of them are “...
8
votes
2answers
842 views
Wait, it is worth it?
You went to a Casino, and saw a quite interesting stall.
The cardboard besides the stall says:
You first pay \$$5$
You have to toss the fair coin. If it lands heads, you can ...
15
votes
4answers
1k views
Random walking on a board
There’s a pawn starting in the center of this game board. At each move, it can advance randomly towards any of the adjacent squares sharing a common side with equal chance. What’s the probability of ...
0
votes
0answers
54 views
A Dices Probability Riddle [duplicate]
Bob (A), Steven (B) and Joe (C) were playing with dices, each one of them made his own dice and wrote a number between 1-6 on each side of his dice.
After playing for a while they've noticed that :
(...
1
vote
0answers
98 views
full unmatch probability [closed]
You have 5 distinct color envelops and 5 distinct color letters. You randomly put one letter in each envelop. What is the probability of no pair matching in color?
I can find the answer with brute ...
8
votes
1answer
305 views
Frog in the Well [duplicate]
A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
5
votes
1answer
153 views
Not a coincidence
Your company has successfully made 140 sales since they started promoting the new product. The other owner, who is very superstitious, notices that today is the 140th day of the year, and believes ...
5
votes
2answers
244 views
Achieve the best outcome by a tactical statement
This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
2
votes
0answers
107 views
Probabilities for “What number is that? — asks grandpa”
Inspired from Multilanguage generalization of "What number is that? Asks Grandpa" and What number is that ? Asks Grandpa
In this puzzle we will use the English alphabet of 26 letters. We ...
2
votes
1answer
95 views
Ideal number of Fruit Baskets
I'm not sure if this is more of a Math or a Puzzling question, but I'll give it a shot here due to it's game related aspects and rules. I've been playing some Runescape lately and while training the "...
7
votes
1answer
194 views
The sadistic chieftain and the lethal truel game
In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind.
"I'll ...
8
votes
4answers
442 views
Which gun is Alice's best choice?
Alice, Bob and Charles are involved in a deadly three way duel game.
Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
9
votes
5answers
319 views
Find the optimal strategy for this dice game
You are playing a game: You have $6$ standard 6-sided dice that are all rolled at the start of the game. The sum of dice values is your score. Each turn, you can take any (or none) dice and reroll ...
6
votes
1answer
144 views
Darwin Fooling Dalton
Dalton wants to measure the effectiveness of a treatment for a particular type of plant and, being a good scientist, decides to have a control group that does not have the treatment.
He is able to ...
1
vote
2answers
149 views
Cheapest strategy on average to find specific items in a set
The problem
You have a set on N (around 15-30) seemingly-identical objects, which in fact comprises a small number D (unknown, between 1-3) of defective objects and the rest (N-D) are good.
There is a ...
13
votes
3answers
1k views
Football Rivals
Team A and Team B are perennial football rivals. Every year they meet for a series of games. The first team to win four games gets to take home the Golden Teapot and keep it for a year.
The teams are ...
3
votes
1answer
90 views
Does it exist a quick way to find the numbers unseen of two tokens after then have been tossed? [closed]
I'm confused about this riddle. I've tried to guess which numbers could be on bottom, but in the end I couldn't got an answer. Can someone help me please?
The riddle is as follows:
Over a table ...
7
votes
1answer
167 views
Guessing the coin flips [duplicate]
Two prisoners, Alice and Bob, are captured by a dragon and placed in separate, isolated cells. The dragon then flips an infinite number of fair coins, and tells the outcomes of odd throws to Alice and ...
6
votes
2answers
251 views
A very tiny probability puzzle [closed]
Imagine there are six football teams (A,B,C,D,E,F). They play each other in a league once only (on neutral ground).
To determine the score, two $d4-1$, i.e. the outcome is $\{0,1,2,3\}$ are rolled, ...
2
votes
1answer
143 views
Four unfair dice
On a table there are four standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each.
Alice starts and chooses a die. Then Bob chooses a die and both throw the dice.
The winner is the person ...
1
vote
1answer
124 views
Banknotes recalling [closed]
Last year the inhabitants of Elfland (which are -of course- Elfs) had a referendum and decided to stop using barter and to adopt their own currency (the Elfcoin).
On January 1st, 2020 the central ...
4
votes
2answers
457 views
Gambling snap game
You have two shuffled decks of cards (52 cards each).
You put them next to each other and deal two at a time, one from each deck.
What is the probability that there will be at least one match? ...
3
votes
1answer
176 views
Two dice with same probability for each sum mk2
Inspired by Two dice with the same probability for each sum?
To cheat in a game of sums, you get yourself a pair of magic dice. That pair behaves in a wonderful way where each individual die is fair (...
5
votes
6answers
1k views
Two dice with the same probability for each sum? [duplicate]
A friend invites you to play a game. The game is using two standard six-sided dice with faces numbered 1, 2, 3, 4, 5, 6 each.
As usual, the dice are considered distinguishable, i.e. throwing a 1 with ...
8
votes
1answer
258 views
Maximizing Product of Selected Cards
Jennifer is playing a game. The Ace through King of spades are taken from a standard playing deck and laid out facedown on the table. At any time, Jennifer can select two cards and reveal them, and ...
9
votes
3answers
422 views
A box full of unfair coins
Lolek and Bolek are arguing on whose turn is to take out the trash.
They have a box with $n$ coins. when the coin $i$ is thrown, the probability that it lands on heads is $p_i$.
They decided to make ...
1
vote
3answers
203 views
Blood Type Puzzle 2: Am I Pure Blood?
This puzzle is similar to the first puzzle but with a few twists:
In this question:
both my mom and I are blood type B.
But this time I don't know my dad's blood type.
My mom said her parents ...
3
votes
3answers
276 views
Blood Type Puzzle 1: Am I Pure Blood?
If my parents (biological) and I all have blood type B, how likely am I a pure blood? (expressed as a percentage)
Follow up question: If my dad is blood type AB instead of blood type B, and ...
6
votes
1answer
318 views
Russian Roulette (Redux!)
You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will ...
1
vote
2answers
260 views
Find the least number of objects from a jar when those have two colors
I've been going in circles with this question which belongs to certainty about something. The original source of this problem is unknown. I found it in a textbook who doesn't have an author but rather ...
-3
votes
2answers
152 views
Chef wants to play [closed]
You are very hungry and decide to visit a restaurant with a couple of friends. You want to order three dishes for the three of you. But, the chef serves you only if the total cost of the dishes ...
1
vote
1answer
100 views
Variation of Monty Hall problem for gambling on who is the champion soccer team
So let's say, if you can guess who the champion team is for soccer, such as in World Cup, then you win a car. Otherwise, you win a goat.
There are 4 teams left. Country A, B, C, and D.
And country A ...
7
votes
3answers
169 views
Playing Chess Game of Chance
I still enjoy playing chess at the age of ninety four.Those contemporary opponents I used to play with have all passed away without me even getting even scores with any of them. On my spare time I ...
0
votes
2answers
297 views
Witches' Coffee [closed]
Two witches make a nightly visit to an all-night coffee shop. Each arrives at a random time between 0:00 and 1:00. Each one of them stays for exactly 30 minutes. On any one given night, what is the ...
2
votes
1answer
162 views
Sleeping Beauty Study at the Institute of Mad Science [closed]
You've been approached to assist in the furtherance of SCIENCE as a research subject at the Institute of Mad Science (local branch)!
The experiment you'll be involved with is called the Sleeping ...
16
votes
3answers
1k views
Box of tablets, whole or broken: solution required
This is a puzzle that I thought up whilst taking a course of meds. I currently haven’t solved it, and would be curious to know if anyone has a solution for it. Here goes:
Scenario:
John has a box of ...
1
vote
1answer
82 views
Chess Puzzle to calculate the minimum number of movements of pawn [closed]
Given an N×N chessboard, with two pieces, a black pawn and a white pawn randomly placed on the chessboard. What is the minimum number of steps required by the white pawn to reach the black pawn under ...
10
votes
1answer
324 views
Birthday girl's casino game
My daughter's birthday is coming up. Here's a fun party game we can play to celebrate. (Bring your wallet!)
I have a pair of 6-sided dice, and a standard deck of 52 cards.
You place your ...
5
votes
3answers
210 views
When is the truth spoken?
A thief speaks truth two days a week alternatively ( T F T ). The days are the same for each week. The thief gives these statements on 3 consecutive days :
D1 : I lie on Monday and Tuesday.
D2 : It'...
