Average number of different colors of marbles in a sample?

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Discussion Overview

The discussion revolves around the expected number of different colors of marbles in a sample drawn from a bag containing multiple colors, specifically framed in the context of probability theory. Participants relate this to a scenario involving DNA amplicons and seek clarity on the underlying concepts of probability and expectation.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents a scenario involving a bag of 10 different colors of marbles, asking how many different colors would be expected in a sample of 12 drawn with replacement.
  • Another participant provides a link to a resource that presumably contains the answer to the posed question.
  • A participant expresses gratitude for the tutorial and indicates a willingness to understand the concepts further.
  • A later reply mentions the expected value formula, denoting it as ##E(V)##, with parameters ##m=10## and ##n=12##, but does not clarify the calculation process.

Areas of Agreement / Disagreement

The discussion does not present a consensus on the expected number of colors, as participants are still exploring the concepts and calculations involved.

Contextual Notes

Participants have not fully resolved the mathematical steps needed to arrive at the expected value, and there may be dependencies on definitions of probability and expectation that are not explicitly stated.

JS-Student
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Hi, I'm asking this in relation to samples of DNA amplicons, but I'm so confused by probability, that I think it would be easier for me to understand in terms of simple marbles-in-bag situation.

Say there is a bag of 10 different colors of marbles in equal amounts, and you are allowed to pull out 12 marbles, each time with replacement. In your sample of 12 marbles, how many different colors of marbles would you expect to have?

If someone could walk me through this, especially the concepts necessary to figure this out, I would greatly appreciate it.
 
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Thank you, I will try to understand this tutorial.
 
JS-Student said:
Thank you, I will try to understand this tutorial.

Please do ask if something is unclear. The result you want is ##E(V)## in ##19##. The values are ##m=10## and ##n=12##.
 

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