# 50/50 Chance

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• November 20th 2010, 04:41 PM
Galaxy
50/50 Chance
Hello there folks!

I was in a pretty serious debate with my friend about probability:

You have 2 cards: 1 red and 1 blue.
You have 1 chance to pick blue, then you mix the cards.
It's either: you always pick blue, you pick blue n-times, you never pick blue.
Let's say that time is infinite.

How can I proove that you MUST pick blue at least once in infinite time?
• November 20th 2010, 04:48 PM
dwsmith
• November 20th 2010, 04:48 PM
Archie Meade
Quote:

Originally Posted by Galaxy
Hello there folks!

I was in a pretty serious debate with my friend about probability:

You have 2 cards: 1 red and 1 blue.
You have 1 chance to pick blue, then you mix the cards.
It's either: you always pick blue, you pick blue n-times, you never pick blue.
Let's say that time is infinite.

How can I proove that you MUST pick blue at least once in infinite time?

Why can't you keep getting red ?
• November 20th 2010, 04:53 PM
Galaxy
Quote:
I'm sorry, I don't understand it. I'm still in high school.

@Archie Meade
I have to proove that you MUST, at least once in infinite time, get a blue card. The probability is 50/50, a 0.5 factor. If you aggregate 0.5 with 1/2 of 0.5 and repeat this forever, you will get number 1 (at least in infinite time). Can this be considered as a proof?
• November 20th 2010, 05:46 PM
dwsmith
The Law of Large Numbers: if you do an event over and over again, the results will tend to the average. The average is 50/50. Therefore, for example, if we do the event 100 times, our results should be roughly 50/50. We could have 45 blues and 55 red, 55 blue and 45 red, 49 blue and 51 red, ......
• November 20th 2010, 05:46 PM
Archie Meade
Quote:

Originally Posted by Galaxy
I'm sorry, I don't understand it. I'm still in high school.

@Archie Meade
I have to proove that you MUST, at least once in infinite time, get a blue card. The probability is 50/50, a 0.5 factor. If you aggregate 0.5 with 1/2 of 0.5 and repeat this forever, you will get number 1 (at least in infinite time). Can this be considered as a proof?

$0.5+0.5^2+0.5^3+0.5^4+.................+0.5^n=\dis playstyle\frac{0.5\left(1-0.5^n\right)}{0.5}$

approaches 1 as n approaches infinity.

It's not a proof as such, because mathematically speaking, you cannot treat infinity as a value.
You can calculate limits though.

This is all ahead of you at present.

The only way you "must" get a blue is if you can rule out, via some condition, a never-ending string of reds.