Probability of matching n words with n pictures correctly

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Discussion Overview

The discussion revolves around determining the probability of matching n words with n pictures correctly, specifically focusing on the probability function for having exactly y words match correctly. The scope includes theoretical exploration and mathematical reasoning.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant poses the question of the probability function for matching y words correctly with n pictures.
  • Another participant suggests that the sorting method of words and pictures affects the probability, proposing a method involving cards that are shuffled and dealt.
  • A participant mentions the initial probability of the first card having a 1/n chance of matching correctly, noting complications if the first card is incorrect.
  • There is a reference to a common analogy of seating dinner guests according to place-cards to illustrate the problem.
  • A later reply introduces the concept of using the hypergeometric distribution to find a solution.
  • One participant mentions the "Rencontres numbers" as a potential answer and provides a link to a Wikipedia entry for further details.

Areas of Agreement / Disagreement

Participants express varying views on the sorting method and its implications for the probability calculation. There is no consensus on a definitive solution or approach, and multiple perspectives on the problem remain present.

Contextual Notes

Some assumptions regarding the sorting method and the implications for probability calculations are not fully explored. The discussion includes references to mathematical concepts that may require further clarification.

BifSlamkovich
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Suppose there are n pictures and n words. Each word matches with exactly one out of the n pictures. What is the probability function of having exactly y words match up correctly?
 
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Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?
The first card has a 1/n chance of being next to the right picture - but, if it is wrong, then another card is guaranteed to be next to a wrong picture. That will be your problem.

Anyway - this sort of thing is commonly described as seating dinner guests against their place-cards.
 
Simon Bridge said:
Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?

Yes.
 
Simon Bridge said:
Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?
The first card has a 1/n chance of being next to the right picture - but, if it is wrong, then another card is guaranteed to be next to a wrong picture. That will be your problem.

Anyway - this sort of thing is commonly described as seating dinner guests against their place-cards.

Do you know the solution? I can write one, but mine gets more complicated as n increases.]

Edit: Can you use the hypergeometric distribution to get the answer?
 

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