# Drawing cards...

• Sep 26th 2010, 10:23 PM
owq
Drawing cards...

1. In a game, a pile of 3 poker cards(could be any suit or points) were presented to Rachel, faced down. Rachel randomly drew a card and kept it. Now, a full deck of 52 cards is presented to her. She is asked to take a card randomly. She wins a prize if the card she takes is of the same suit as the card she drew earlier. What is her chance of winning a prize?

For this, what I think is that it doesn't matter what the 3 poker cards were, since she already drew it. So the chance of picking the same suit as the card she drew is 13/52? Is that right?
• Sep 26th 2010, 10:45 PM
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Quote:

Originally Posted by owq

1. In a game, a pile of 3 poker cards(could be any suit or points) were presented to Rachel, faced down. Rachel randomly drew a card and kept it. Now, a full deck of 52 cards is presented to her. She is asked to take a card randomly. She wins a prize if the card she takes is of the same suit as the card she drew earlier. What is her chance of winning a prize?

For this, what I think is that it doesn't matter what the 3 poker cards were, since she already drew it. So the chance of picking the same suit as the card she drew is 13/52? Is that right?

Edit: I did not think it out well enough; awkward and the OP are right. Original message follows.

well technically we are never told whether the 3 cards are chosen randomly, nor whether they can be duplicate cards from multiple decks, but this is likely just an imprecision of the language. assuming the 3 cards are randomly chosen from a deck, then the probability of winning is just 1/4 as you say.
• Sep 27th 2010, 02:05 PM
awkward
Actually, I think it's not necessary to make any assumptions about the way the 3 initial cards were chosen in this problem.

Rachel has drawn either a diamond, club, heart, or spade; and in any case the probability of matching the suit is 13/52.
• Sep 27th 2010, 02:20 PM
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Quote:

Originally Posted by awkward
Actually, I think it's not necessary to make any assumptions about the way the 3 initial cards were chosen in this problem.

Rachel has drawn either a diamond, club, heart, or spade; and in any case the probability of matching the suit is 13/52.

You're right! Very silly of me.