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July 17th, 2011, 01:02 PM  #11  
Global Moderator Joined: May 2007 Posts: 6,755 Thanks: 695  Re: Probability. A deck of card Quote:
 
July 17th, 2011, 01:10 PM  #12 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond  Re: Probability. A deck of card
I see, thanks. I was thinking that if you shuffle a deck of cards the odds of a queen of spades on the bottom would be 1/52 and 1/52 for a jack of clubs on top. It is interesting the sums of probabilities work out to 1 when added, using either interpretation. The results are close too.

July 17th, 2011, 01:45 PM  #13 
Newbie Joined: Jul 2011 Posts: 16 Thanks: 0  Re: Probability. A deck of card
The probability for either is 1/52, but if we're creating a case where both happen then one unknown card has become known and there are only 51 possibilities for the second. The probability of all possibilities in a situation sums to 1 (as it always should afaik), you are just describing a different situation. In yours a card is checked, then replaced and the deck is shuffled again before checking the second card. In the original a card is checked, but the deck is not shuffled before checking the other card. That means when we check the other side of the deck, we already know the card that occupied the top of the first side, so there's only 51 possible cards that could be the second card. 
July 17th, 2011, 01:53 PM  #14  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,934 Thanks: 1128 Math Focus: Elementary mathematics and beyond  Re: Probability. A deck of card Quote:
 
July 17th, 2011, 06:29 PM  #15 
Global Moderator Joined: Dec 2006 Posts: 20,622 Thanks: 2074 
If the top card is queen of spades, the chance that the bottom card is queen of spades is zero. The chance that the top card is not queen of spades and the bottom card is queen of spades is (51/52)(1/51) = 1/52, as expected. 

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