Explain/solve the Matching Problem in the simplest terms

  • Thread starter Thread starter redphoton
  • Start date Start date
  • Tags Tags
    Terms
Click For Summary
The "Matching Problem" often refers to scenarios where items from one set must be matched with items from another, such as the classic example of an absent-minded secretary randomly stuffing letters into envelopes. The probability of a match occurring can be calculated by determining the probability that a match does not happen, denoted as P, and then using the formula 1-P for the probability of a match. This problem can be explored through various mathematical approaches, including graph theory and combinatorics. Understanding these concepts helps clarify the complexities of matching in different contexts. The discussion emphasizes the importance of probability in solving matching problems.
redphoton
Messages
12
Reaction score
0
Explain/solve the "Matching Problem" in the simplest terms

How would you explain and solve the "Matching Problem" to a HS math club? give the simplest explanation and solution you know.
 
Last edited:
Physics news on Phys.org


You mean the stable matching problem, from graph theory?
 


matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."
 
Last edited:


There are many different problems involving matching one set against another.
 


redphoton said:
matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."

If P is the probability that a match DOESN'T happen, then 1-P is the probability that a match happens. Is this what you want?
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
View full post »

Similar threads

Undergrad Please Explain (actually explain) The Monty Hall Problem
  • · Replies 53 ·
2
Replies
53
Views
2K
Graduate Parameter optimization for the eignevalues of a matrix
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Is there a term for this type of unknown experimental interference?
  • · Replies 2 ·
Replies
2
Views
964
High School Calculating Odds of Getting at Least One Pair in Pai Gow
  • · Replies 18 ·
Replies
18
Views
3K
MHB What Do H and * Symbols Mean in Epp's Discrete Math Textbook?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
4K
Graduate Area distribution of inscribed triangles in a circumference
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Causal inference developed by Pearl
  • · Replies 40 ·
2
Replies
40
Views
5K
MHB Show Inequality: Explain Why $g(k) \geq \frac{3^k}{2k+1}$ in Football Matches
  • · Replies 7 ·
Replies
7
Views
2K
MHB Solving Q.7 with Truth Tables: What Is the Right Conclusion?
  • · Replies 2 ·
Replies
2
Views
2K