Comment author:omeganaut
12 May 2011 05:38:46PM
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"Or here's a very similar problem: Let's say I have four cards, the ace of hearts, the ace of spades, the two of hearts, and the two of spades. I draw two cards at random. You ask me, "Are you holding at least one ace?" and I reply "Yes." What is the probability that I am holding a pair of aces? It is 1/5. There are six possible combinations of two cards, with equal prior probability, and you have just eliminated the possibility that I am holding a pair of twos. Of the five remaining combinations, only one combination is a pair of aces. So 1/5."
For future reference the initial phrase "I have four cards" may imply that you have in your possession those cards already. Combined with the fact that you draw two cards afterwords implies that you now have six cards. The simple fact that you are using cards implies that you are using a full deck of 52 cards, unless you specifically say there are only certain cards in play. I just want to clear that up because I had to reread that section a few times before I understood how you came up with your figures.

Comment author:thomblake
12 May 2011 10:20:49PM
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The standard way of quoting is to use a single greater-than sign (>) before the paragraph, and then leave a blank line before your response. Note the 'Help' link below the comment editing box.

## Comments (186)

Old"Or here's a very similar problem: Let's say I have four cards, the ace of hearts, the ace of spades, the two of hearts, and the two of spades. I draw two cards at random. You ask me, "Are you holding at least one ace?" and I reply "Yes." What is the probability that I am holding a pair of aces? It is 1/5. There are six possible combinations of two cards, with equal prior probability, and you have just eliminated the possibility that I am holding a pair of twos. Of the five remaining combinations, only one combination is a pair of aces. So 1/5." For future reference the initial phrase "I have four cards" may imply that you have in your possession those cards already. Combined with the fact that you draw two cards afterwords implies that you now have six cards. The simple fact that you are using cards implies that you are using a full deck of 52 cards, unless you specifically say there are only certain cards in play. I just want to clear that up because I had to reread that section a few times before I understood how you came up with your figures.

The standard way of quoting is to use a single greater-than sign (>) before the paragraph, and then leave a blank line before your response. Note the 'Help' link below the comment editing box.