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July 30th, 2019, 09:14 AM   #1
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Percentage experiment/question

Hello,

I did an experiment today, and I wanted to share all of it with you. Involve mathematics, percentage to be in fact. Here's what I did.

I have a marbles collection. I decided to take out nine green Marbles and one clear marble out of that collection and put it in a bag. I told myself "your goal is to get the clear marble. draw one marble at a time, then figure out how much the chance of getting the clear marble increases."

So, 10 marbles, one is a clear marble, the rest are green. The chance of drawing the clear marble is 10% let's say you draw marble, and it's a green one. The chance on the next draw of drawng the clear marble have risen from 10 percent to 11.111111..... percent. Draw another marble, it's green. Chances of drawing the clear on the next draw is 12.5 percent.

Keep on going, until you draw the last marble, which turned out to be the clear one. The numbers go as follows for the chances of getting the clear marble.

1st draw, 10%
2nd, 11.11111....%
3rd, 12.5%
4th,14.2857143....%
5th, 16.666666....%
6th, 20%
7th, 25%
8th, 33.333333....%
9th, 50%
10th and finally, 100%

So, I put these numbers on graph paper. And I charted the growth of the chances of drawing the clear marble from the first draw to the final draw. To my surprise, a very familiar curve showed up. I looked at it, and I recognized it right away. I thought to myself the following:

"e?"

To sum it up, here's what I learned, and please correct me if I am wrong.

Euler's number, can function with probability if you have a certain amount of marbles, and you draw one, and the chances of getting the one you're looking for increases.

Am I correct?

Jared
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July 30th, 2019, 11:02 AM   #2
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No.
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July 30th, 2019, 01:00 PM   #3
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@skipjack, would you mind telling me how I am not correct? I am curious.
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July 30th, 2019, 01:30 PM   #4
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Your values -- the probability of the next marble being clear if you have already drawn n green marbles -- are 1/(10-n). 1/10, 1/9, 1/8, 1/7, …

You are basically following the y = 1/x curve from right to left at integer values. While this curve does grow extremely fast at one end (in fact, asymptotically approaches infinity as x goes to zero), it is not the same as the exponential function e^x.
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July 30th, 2019, 01:46 PM   #5
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Thank you, very much. I see it now. Thanks so much for helping me understand this! I guess I got confused when the curve looked like the e curve on my graph paper.

Again, thank you for helping me understand this, I appreciate it. I guess I still have a lot to learn!

Regardless of the outcome, it was still an interesting experiment in my own opinion.

Jared
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