Questions tagged [puzzle]
Use this tag for statistical puzzles that challenge the ingenuity of the solver. (Do not use the tag "games" for this purpose.)
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In the Monty Hall problem, does it matter that the host knows which door the car is behind? If so, why?
If I'm thinking about this correctly, regardless of how the host chooses which door to open, there's a 1/3 chance the player initially picks the door with the car behind it, in which case they shouldn'...
2
votes
1
answer
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How to correctly compute conditional probabilities by considering the probability of each possible outcome?
So I've been trying to understand the
boy-girl paradox, and I reframed it in terms of coin flips to help it make more sense to me and I get now why the probability is different depending on whether we'...
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How to resolve the ambiguity in the Boy or Girl paradox?
Specifically, I was reading this article, which discusses this wording of the question:
Consider a family with two children. Given that one of the children is a boy, what is the probability that both ...
3
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2
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Finding the optimal stopping time to place a bet in an urn problem
This question is a spin on the question Basic probability question but struggling (brain teaser with friend) but with some additional rules and considerations that make it more complex. The ...
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2
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How many rounds to visit every place on a Monopoly style game board
I see some kids playing on a circular gameboard trying to visit every field and I wonder how long it will take before they finish.
I can simulate it like below, but is there possibly an elegant ...
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Probability of a similar sub-sequence of length X in two sequences of length Y and Z
Say we have two random sequences of length $y=3300$ and length $z=26$, where the sequences are made out of a combination of $k=4$ four letters ACGT.
the letter in each position of the sequence is ...
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(Open-ended?) Stat puzzle about expected value
A fair coin is flipped $200$ times and each time it lands on heads, $1$ dollar is added to a pot. After this process is over, an auction is held for the pot. There is exactly one other person at the ...
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Measuring sticks to minimize error
I encountered the following problem while preparing for an interview:
There are two sticks $A$ and $B$ with different lengths. In addition, you are given a ruler. However, the ruler is not perfect: ...
user298588
9
votes
1
answer
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Modified sleeping beauty paradox
Consider the following classic problem:
Some researchers would like to put Sleeping Beauty to sleep on Sunday. Depending on the secret toss of a fair coin, they will briefly awaken her either once ...
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Stats Puzzle About Random Guesses [closed]
If you are told to guess a number between 1 and 100 that is as close as possible to the standard deviation of the guesses of others who are told the same thing, what number would you guess?
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Normal Distribution Puzzle/Riddle
Some time in the future, a lottery takes place, with winning number N. 3 of your friends from the future, John, Joe, and James, provide you with guesses on the number N.
John's guess a is randomly ...
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The frog problem with negative steps
Standard Problem description
In this question The Frog Problem (puzzle in YouTube video) a frog has to jump from leaf to leaf on a row of leaves. And the question is how long it takes on average to ...
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The Frog Problem (puzzle in YouTube video)
There is an interesting puzzle in YouTube video Can you solve The Frog Problem?. I'll try to give an equivalent formulation here.
A frog is on one side of the pond and wants to get on the other side. ...
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votes
1
answer
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Old race car problem/puzzle
This was in an old (1935) "brain teaser" book, and I can't figure it out how to solve it!
There's a car race during which the cars experience 4 different types of car trouble, e.g. flat tire, blown ...
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Did Statistics.com publish the wrong answer?
Statistics.com published a problem of the week:
The rate of residential insurance fraud is 10% (one out of ten claims is fraudulent). A consultant has proposed a machine learning system to review ...
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1
answer
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Value iteration does not converge when using Q learning
I have a simple game and want my agent to play it with a help of reinforcement learning. We have a board and a value in each cell. The goal is to go from start to finish point with the highest score (...
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Fraction / Percentages Brainteaser
In my business math class, the instructor put up the following case study, and asked us to find any flaws in the logic, but, I have been unable to see what is wrong with the following argument:
"A ...
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Probability of having 2 girls and probability of having at least one girl
In this question the general formula P(A|B) = P(A ∩ B)/P(B) is used. I understand through intuition why the answer should be 1/3. What I don't understand is why P(both girls, at least one girl) is 1/4....
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1
answer
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Expected payoff vs. payout for expected outcome
Someone pointed out this puzzle in Kahneman's Thinking, Fast and Slow. I paraphrase.
A game rewards participants based on how long it takes to obtain the first heads in a toss of a fair coin. If ...
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votes
1
answer
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need intuition: why is there no winning strategy to this game?
I have 1000 cards on the table, R1 are red and B1 are blue.
You have 1000 tokens on the table, ...
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Uniform random variables and optimal strategy
This comes from Fivethirtyeight's riddler weekly challenge...
Toddler poker is played by two players. Each is dealt a “card,” which
is actually a number randomly chosen uniformly from the ...
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Probability puzzle solved by R simulation; answer close but not exactly. Bug in my code? [closed]
Here's an interesting probablity puzzle:
One hundred people line up to board an airplane. Each has a boarding
pass with assigned seat. However, the first person to board has lost
his boarding ...
- 1,081
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votes
0
answers
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Maximize the difference of the means of two sets
I have a set of real numbers which I'll call set A. I have a threshold t. I have sets B and <...
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Optimal strategy for a simple game
Let's say I'm playing a game that works likes this: I have n bowls that are each filled with a different number of marbles, and I know how many marbles are in each bowl. At each round, the dealer goes ...
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Modified German Tank problem involving string distance metrics
Pretend we have a list of items, e.g. names, and we know it is sorted ALPHANUMERICALLY let's say in ascending order. Given a small set of the first K items, how can we estimate the length of the full ...
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Will there ever be an unhappy Tribble in Oz?
Here's an amusing problem brought to me by a student. Although it was originally phrased in terms of mutually annihilating bullets fired at regular intervals by a gun, I thought you might enjoy a ...
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1
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Ticket selling probability puzzle
I was talking with a friend of mine about a simple statistical puzzle that we weren't able to solve due to our ignorance about the statistics world.
Consider a ticket selling web. A musical event is ...
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0
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Puzzles using Kolmogorov's zero–one law
Do we have any interesting puzzles/problems using Kolmogorov's zero-one law? Maybe a classic brain teaser or problems like those in Fifty Challenging Problems in Probability?
18
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7
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Two envelope problem revisited
I was thinking of this problem.
http://en.wikipedia.org/wiki/Two_envelopes_problem
I believe the solution and I think I understand it, but if I take the following approach I'm completely confused.
...
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votes
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How to solve Chuck-a-Luck puzzle
Story (spoilers!)
The puzzle:
Chuck-a-Luck is a gambling game often played at carnivals and gambling
houses. A player may bet on any one of the numbers 1,2,3,4,5,6. Three
dice are rolled. If ...
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6
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Statistics library with knapsack constraint
Suppose you had $200 US to build a (very) small library of statistics books. What would your choices be? You may assume free shipping from Amazon, and any freely available texts from the internet are ...
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15
answers
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The Monty Hall Problem - where does our intuition fail us?
From Wikipedia :
Suppose you're on a game show, and
you're given the choice of three
doors: Behind one door is a car;
behind the others, goats. You pick a
door, say No. 1, and the host, who
...
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