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If I put 4 green rabbits and 1 red rabbit into a hat, that's 5 rabbits!

I then make 5 attempts at pulling the red rabbit out of the hat.

If I get a green rabbit I put it back in the hat.

On the first attempt I have a 1 in 5 chance of red rabbit success.

If the first attempt fails, on the second attempt I still have a 1 in 5 chance of red rabbit success.

What is the unlikelihood that I will fail to pull out the red rabbit in 5 attempts?

Although I may never succeed, Is there some magic that makes it more likely that I will get the red rabbit over time?

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up vote 4 down vote accepted

Each time you have $\frac{4}{5}$ chance of getting a green rabbit. As the events are independent, for $n$ tries you have $\left(\frac{4}{5}\right)^n$ chance of never getting a red rabbit.

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If you try long enough, you may have more rabbits, which will perturb the probability. –  Ross Millikan Mar 18 '11 at 1:47
    
True, I hadn't thought of that. –  Grokodile Mar 18 '11 at 12:21
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