Probability of Group Repetition in 8 Groups with 16 People

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Homework Help Overview

The discussion revolves around calculating the probability of group repetition when forming 8 groups of 2 people each from a pool of 16 individuals. The original poster seeks to understand the likelihood of specific pairings occurring across multiple trials.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of forming groups, specifically questioning whether the selection is random and how that affects the probability calculations. There is mention of empirical results from repeated trials.

Discussion Status

The conversation is ongoing, with participants exploring the implications of random selection on probability. Some guidance has been offered regarding the need for clarity on the grouping method, but no consensus has been reached on the calculations or interpretations.

Contextual Notes

Participants are considering the randomness of group selection and its impact on the probability of repetition. There is a reference to specific empirical findings, but the exact methodology for calculating probabilities remains under discussion.

courtrigrad
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Lets say you have 16 people. You want to make 8 groups. There are 2 people per group. What is the probability that 1 of the 8 groups is the same for a certain number of trials? For example, if person A is with person B this trial, what is the probability that person A will be with person B in the next trial (or many more trials after that)? I know the probability of all the groups being the same is [tex]\frac{1}{120}[/tex].

Thanks
 
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It was also empirically discovered that the probability of at least one group being the same was 0.4778 . This result was discovered by repeating the experiment 100,000 times.

Anyway thanks a lot

:smile:
 
One of the things you will need to do before this can be answered is say HOW you are making the groups. Are you picking people at random (each person equally likely to be chosen)?
 
yes the groups are chosen at random.
 
So if its random, then each group has an equal chance . The probability needs to be a fraction that equals 0.477.

Any help is appreciated

Thanks
 
any ideas?
 

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