All Questions
62
questions
3
votes
1
answer
82
views
You pick $N$ positive integers between $1$ and $M$ without replacement. If you add another number, what is the probability the maximum hasn't changed?
You initially start with all the integers between $1$ and $M$. You then pick $N$ of them randomly, without replacement, to generate a new set of $N$ non-repeating numbers. The maximum of this set is $...
4
votes
0
answers
144
views
No two adjacent bulbs on
The problem is to count number of configuration of $9$ bulbs on a $3\times 3$ grid, where no two bulbs that are adjacent are switched on.
I solved this problem in a very ad-hoc kind of manner, the ...
- 378
1
vote
1
answer
210
views
The toys problem: Probability of getting two matching good item and a different third Item
I've encountered an intriguing probability problem. I just registered to ask this, so this will be my first post.
Disclaimer: I met this problem in a real setting that's it too convoluted to explain (...
- 13
1
vote
1
answer
141
views
100 prisoners riddle - Dependency of probabilities
I am referring to the well-known riddle of the title (if you don't know what I am talking about here it is: https://en.wikipedia.org/wiki/100_prisoners_problem - See sections "Problem" and &...
- 13
4
votes
0
answers
109
views
What percent of lighted grids are walkable: a trick-or-treating problem
I am a math teacher that likes to invent fun math problems to explore. Here is one I have been investigating for a little while and have made little progress on because the number of possible $n \...
- 53
5
votes
2
answers
189
views
How to count - probability puzzle
A $3 \times 3 \times 3$ big cube consists of $1 \times 1 \times 1$ smaller cubes. The big cube is painted black on the outside. Suppose we disassemble the cube and randomly put it back together. What ...
- 5,450
4
votes
3
answers
218
views
Evaluating $\sum_{r=0}^{1010} \binom{1010}r \sum_{k=2r+1}^{2021}\binom{2021}k$
I need to find the summation
$$S=\sum_{r=0}^{1010} \binom{1010}r \sum_{k=2r+1}^{2021}\binom{2021}k$$
I tried various things like replacing $k$ by $2021-k$ and trying to add the 2 summations to a ...
- 43
1
vote
2
answers
633
views
What is the optimal strategy for the "100 prisoners problem" when waiting prisoners are told how many drawers the currently active prisoner has opened
Introduction: A description of the original problem can be found on Wikipedia. The best strategy is: each prisoner opens the drawer with their number first and then each subsequent drawer is ...
- 211
0
votes
3
answers
281
views
Expected number of cards drawn to get two consecutive aces
Here is a question from my probability textbook:
A person draws cards one by one from a pack and replaces them till he has drawn two consecutive aces. How many cards may he expect to draw?
I'm not ...
- 1,415
4
votes
1
answer
229
views
In a tournament of $2^n$ people, what is the probability of player $i$ and player $j$ meet at $k$-th round
In a knock-out tournament of $2^n$ people, where if $i < j$, player $i$ is better than player $j$ and will beat her in any parts of the tournament. What is the probability of player $i$ and player ...
- 834
10
votes
3
answers
284
views
How would you go about learning the combination of coins the man has?
I am trying to identify the branch of math that would help to solve the following problem:
A man has picked $10$ coins out of a bag and has laid them in a row. You cannot see them for yourself, and ...
- 103
4
votes
2
answers
293
views
The Board Football Problem (Part I)
The original question is here (The Board Football Problem (Probability)) and part II is here(The Board Football Problem (Part II)). I was told to segment the question in order to increase the chances ...
0
votes
0
answers
179
views
The Board Football Problem (Probability)
A and B are playing " board football", a two player in which the objective is to score as many goals as possible. As the game does not have any terminating statement, an infinite number of ...
1
vote
1
answer
224
views
What is wrong with my solution to the Monty Hall problem?
I'm trying to develop an intuitive sense of why the suggestion of the Monty Hall problem is that you should switch doors when an informed host opens one of the two dummy doors.
So, I'm trying to think ...
- 73
0
votes
1
answer
2k
views
Probability Puzzle- N letters 2 post boxes [duplicate]
A postman brought N letters to a house with two letter-boxes. Since the two boxes were empty, he puts 1 mail in each of the two mail boxes. Then he chooses one of boxes with probability proportional ...
- 1