Probability paradox?

GRE Quant Problem Solving
1

Shant the answer to this question is D, as the question is about "without replacement" and the probability of red marble changing with each withdraw?

i.e If we get 1st red marble on the 3rd withdraw, the probability of getting red marble on 10th will be different from 1st red marble on the 10th withdraw.
Can anyone elaborate the Prepswift explanation?

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2

Try a smaller example.

3

Aren’t we dividing the number of red marbles by the total number of outcomes (R+B+G)? And as total number of outcomes decrease without replacement, isn’t the probability change with each withdraw?

4

If we try a smaller example:

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When it says “removes the marbles one-by-one”, it means that all marbles will end up being pulled out eventually.

If we list all the ways this can happen, it would look something like this

B, B, B, R, R
B, B, R, B, R
B, B, R, R, B
B, R, B, B, R
B, R, B, R, B
B, R, R, B, B
R, B, B, B, R
R, B, B, R, B
R, B, R, B, B
R, R, B, B, B

What do you notice about the number of times:

  • Red marble is the 3rd one to be pulled out
  • Red marble is the 4th one to be pulled out

Can you try and apply this to your question?