How Likely Are Unlikely Events?

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This discussion centers on the mathematical probabilities of drawing cards from a standard deck and the implications of unlikely events occurring. The calculations demonstrate that drawing multiple cards results in exponentially decreasing probabilities, with the odds of drawing seven specific cards being 1.028 trillion to one. The conversation highlights that while certain events may seem unlikely, they can still occur, especially in scenarios like casinos where numerous card sequences are dealt daily. The conclusion emphasizes that the existence of unlikely events does not negate their possibility.

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skydivephil
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I was thinking about unlikely evenst and conclude they must happen all the time. Imagine I draw a card from a deck, the odds for a particular card to come out= 1/52. Now I replace, shuffle and draw another card, the odds of the sequence of two card are =1/52*1/52 so and we can keep multiplying this by 1/52 for each card if we repeat the process:
2 card = 1/2704
3 cards =140,068
4 cards = 7,311,616
5 cards 380,204,032
6 cards =19.77 billion to one.
7 cards = 1.028 trillion to one.

Now presumably casinos are dealing thousands of cards down every day, (Maybe millions?) and so the odds of any particular sequence of cards being dealt is utterly astronimical. So one cannot sy an event cannot happen because its unlikely, it has to be more unliekly than any other event. Anyone disagree with this maths?
 
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I don't disagree with the math, perhaps your argument isn't cogent though.
 
If your aim was to disprove the notion that unlikely events can't happen, you've succeeded.
 
If you could predict the future with 100% accuracy, there wouldn't be any unlikely events. There would only be certain events and impossible events.

EDIT: More precisely, certain or impossible outcomes for a given trial.
 
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