Average number of different colors of marbles in a sample?

[JS-Student]

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.

 

[micromass]

This page contains the answer: http://www.math.uah.edu/stat/urn/Birthday.html

 

[JS-Student]

Thank you, I will try to understand this tutorial.

 

[micromass]

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 $n=12$.