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# 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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3 votes
1 answer
102 views

### Applying Bayesian probability to a generalized Monty Hall problem

I posted this question about the Monty Hall problem and Monty's knowledge of the probability distribution several months ago. I got some good answers and this one in particular helped me gain some ...
15 votes
2 answers
997 views

### The Bing Tibetan Glitch Emoji Problem

Here's a very interesting mathematical statistics puzzle that I randomly stumbled into while using Bing. This turned out to be deep enough that I spent quite some time thinking how one could solve it! ...
3 votes
3 answers
312 views

### 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
39 views

### 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'...
11 votes
3 answers
5k views

### 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 votes
2 answers
210 views

### 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 ...
• 82.1k
3 votes
2 answers
98 views

### 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 ...
• 82.1k
4 votes
1 answer
404 views

### 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 ...
• 82.1k
1 vote
1 answer
747 views

### (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 ...
• 153
1 vote
1 answer
424 views

### 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: ...
9 votes
1 answer
266 views

### 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 ...
• 143
1 vote
0 answers
50 views

### 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?
2 votes
1 answer
316 views

### 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 ...
15 votes
3 answers
2k views

### 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 ...
• 82.1k
9 votes
4 answers
8k views

### 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. ...
• 506
3 votes
1 answer
282 views

### 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 ...
28 votes
2 answers
4k views

### 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 ...
• 383
6 votes
1 answer
2k views

### 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 (...
• 275
2 votes
1 answer
69 views

### 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 ...
• 1,695
4 votes
2 answers
4k views

### 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....
1 vote
1 answer
175 views

### 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 ...
7 votes
1 answer
139 views

### 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, ...
• 3,350
4 votes
1 answer
1k views

### 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 ...
1 vote
1 answer
290 views

### 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 ...
• 1,101
0 votes
0 answers
57 views

### 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 <...
• 55
1 vote
1 answer
99 views

### 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 ...
• 55
3 votes
0 answers
95 views

### 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 ...
• 417
11 votes
1 answer
310 views

### 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 ...
• 328k
1 vote
1 answer
149 views

### 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 ...
• 113
4 votes
0 answers
98 views

### 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 votes
7 answers
6k views

### 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. ...
• 393
7 votes
1 answer
8k views

### 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 ...
• 683
11 votes
6 answers
527 views

### 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 ...
42 votes
15 answers
7k views

### 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 ...