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Let's say there are 12 red 11 green 12 yellow marbles. I pick up 7 marbles randomly. What's the probability of me picking 2 red marbles?

I understand the probability of picking up a red marble is 12/35. How does this relate to picking up 7 marbles and ending up with 2 red ones? I would like an explanation, not just the answer, please.

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    Exactly$2$marbles.2012-09-23

1 Answers 1

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you need exactly $2$ red marbles out of $7$ you chose from a set of $12$ red, $11$ green and $12$ yellow.

No. of ways to choose $2$ red marbles out of $12$ marbles (red)$={12\choose 2}$

No. of ways to choose remaining $5$ marbles out of $23$ marbles (non-red)= ${23\choose 5}$

Total ways of choosing $7$ marbles out of $35$ marbles =${35\choose 7}$

Therefore, Required Probability = $\frac{{12\choose 2}{23\choose 5}}{{35\choose 7}}$

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    Thank you for your help. I have an understanding on this now.2012-09-23