Is this binomial or geometric distribution? And how would you solve this?

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JacobHarris

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A committee of two students will be selected from a list that contains six Grade 9 students and eight Grade 10 students. What is the expected number of Grade 10 students on the committee?
 
It is bad form to post the same question on multiple bulletin boards. It is particularly bad form to show none of your own work. Please do better.
 
2 students? Please enumerate the possible outcomes.
 
What I think should be done is if we use the binomial distribution expected value formula. If we use n=2 and P(S)=8/14. But I think highly that this is wrong
 
JacobHarris said:
What I think should be done is if we use the binomial distribution expected value formula. If we use n=2 and P(S)=8/14. But I think highly that this is wrong
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Why do you think that should be done if you think it is wrong?

Is there anything about this that makes it binomial? Did you notice that the students are selected without replacement?

I would just make a distribution table, as suggested in post #3.
 
JacobHarris said:
A committee of two students will be selected from a list that contains six Grade 9 students and eight Grade 10 students. What is the expected number of Grade 10 students on the committee?
Click to expand...
The title of your post tells me that you are looking for a formula to use rather than using your brain.
If \(X\) is the number of tenth graders chosen then \(X=0,~1,\text{ or }\,2\).
The probabilities are \(\mathscr{P}(X=k)=\dfrac{\dbinom{6}{2-k}\cdot\dbinom{8}{k}}{\dbinom{14}{2}}\)
Now how is the expected number of a particular event defined?
Please post your answer!
 
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