All Questions
76
questions
2
votes
0
answers
50
views
Probability that at least 5 adjacent length-4 blocks of a certain kind occur in a string of 26 random digits
Let a "$(4,2)$-block" be any string of four digits exactly two of which are equal.
Question: What is the probability that in a string of $26$ decimal digits, chosen independently and ...
- 15.1k
1
vote
1
answer
94
views
How to calculated the expected value of the overlap between groups of numbers?
I try to implement a lookup or join like functionality in code, which leads me to the following combinatorial challenge which I fail to tackle in the proper way:
Lets assume I have 50 million numbers, ...
- 113
8
votes
1
answer
133
views
N people in a pit are required to press their kill buttons one at a time, what percentage of the initial population is expected to live on?
I posed this problem for myself based on a simpler problem I saw on reddit, here is the more detailed version of my problem:
The game master traps N people in a pit and equips them with a sort of kill ...
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
0
votes
1
answer
101
views
A dice with numbers 1 to 10 is thrown 4 times. Find the probability that result has 3 consecutive prime or no prime shows up three times consecutively
Here is the exact wording in the problem given.
Numbers from 1 to 10 are printed on a fair 10-faced dice. The dice is thrown 4 times.
Find the probability the result has 3 consecutive prime numbers or ...
- 125
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
4
votes
4
answers
375
views
What is the probability that the sum of 6 four-sided dice is less than or equal to 14?
The solution given is shown below.
My question is how did they count the numerator like that?
What is the explanation for it please?
$$\begin{align}
\frac{C_6^{14}-C_1^6\times C_6^{10}+C_2^6 \times ...
4
votes
1
answer
86
views
Probability that N i.i.d. draws from a multinomial distribution have made all events appear
Consider a multinomial distribution $\mathbb{P}$ on $S$ states $\{s_1,\dots,s_S\}$ where $S\in \mathbb{N}$ and $S\geq 2$, with probabilities $\mathbb{P}(s_i)=:p_i$. Now consider $N$ i.i.d. draws $X_1,...
- 6,779
2
votes
0
answers
54
views
Expected number of balls surrounded by at least one ball of different color
Suppose we have 50 black balls and 50 white balls arranged randomly in a circle. Find the expected number of black balls such that at least one of its neighbors is white.
Proposed solution:
Let $X_i$ ...
- 322
3
votes
3
answers
819
views
What's theoretically a good Nerdle combination?
https://nerdlegame.com/
These are the rules of Nerdle:
There are eight spaces for operators/digits.
Each guess is a calculation.
You can use 0 1 2 3 4 5 6 7 8 9 + - * /or =.
It must contain one “=”.
...
- 31
-1
votes
4
answers
949
views
A stick is broken in three pieces. Find the probability that the resulting pieces are shorter than a certain length. [closed]
A stick has a length of $5$ units. The stick is then broken at two points chosen at random. To find the probability that all three resulting pieces are shorter than $3$.
I tried with complement prob: ...
- 12.7k
3
votes
1
answer
1k
views
Everyone gets a red card
The following cards are dealt with $3$ people at random so that every one of them gets the same number of cards: $$R_1, R_2, R_3, B_1, B_2, B_3, Y_1, Y_2, Y_3$$ where $R$, $B$ and $Y$ denote red, blue ...
- 12.7k
1
vote
2
answers
746
views
What is the Probability of someone meeting a person they know on a train?
My friends and I had a question to calculate the probability of meeting someone you know on the train. So we created a mathematical model question as follows:
A man 'A' travels from a place X to Y. ...
- 15
6
votes
3
answers
837
views
6 Heads Followed by 6 Tails (Coin Flipping)
You throw a fair coin one million times. What is the expected number of strings of 6 heads followed by 6 tails?
The answer given is:
There are $1,000,000 - 11$ possible slots for the sequence to ...
- 73
4
votes
3
answers
198
views
What is the probability of picking a full set from multiset after $m$ draws?
Suppose a bag contains $n$ balls labeled from $1$ to $n$, and suppose I have $k$ of these bags. If I open all of these $k$ bags into an urn, then the urn is effectively a multiset with $kn$ elements: $...
- 7,283