Simple probability problem can’t understand the woreint

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Student108

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Freddy the Ghoul has a special deck of cards that has 54 cards. This deck has the property that if Freddy chooses any 13 cards from it, they will always contain a queen of spades. If Freddy randomly chooses 26 cards from his deck, what's the Smallest number of queens of spades he could have chosen?

I got the answer 2 but let me know what you all get
 
Student108 said:
Freddy the Ghoul has a special deck of cards that has 54 cards. This deck has the property that if Freddy chooses any 13 cards from it, they will always contain a queen of spades. If Freddy randomly chooses 26 cards from his deck, what's the Smallest number of queens of spades he could have chosen?

I got the answer 2 but let me know what you all get
Click to expand...

I'm sorry, but I don't understand your subject line?

Also, we'll be glad to check your work, but we'll need to see it first. Thank you!
 
Student108 said:
Freddy the Ghoul has a special deck of cards that has 54 cards. This deck has the property that if Freddy chooses any 13 cards from it, they will always contain a queen of spades. If Freddy randomly chooses 26 cards from his deck, what's the Smallest number of queens of spades he could have chosen?

I got the answer 2 but let me know what you all get
Click to expand...
How did you get that?

I'd start by deciding how many queens of spades there are in the whole deck. Or, how many cards are not the queen of spades?

What is a "woreint"?
 
Suppose all 54 cards are the queens of spades. Then Freddy would have gotten 13 queens of spades.
Suppose 53 cards were the queens of spades. Then Freddy could have gotten how many queens of spades?
Suppose 52 cards were the queens of spades. Then Freddy could have gotten how many queens of spades?
Suppose 53 cards were the queens of spades. Then Freddy could have gotten how many queens of spades?
...
Suppose 42 cards were the queens of spades. Then Freddy would have gotten how many queens of spades?
Suppose 41 cards were the queens of spades. Then Freddy would have gotten how many queens of spades?
Suppose 40 cards were the queens of spades. Then Freddy would have gotten how many queens of spades?
....
 
stapel said:
I'm sorry, but I don't understand your subject line?

Also, we'll be glad to check your work, but we'll need to see it first. Thank you!
Click to expand...
I request your assistance in discerning the flaw within my reasoning. The initial premise was centered on the observation that a queen of spades appears once within every 13-card subset. Consequently, the inference was drawn that there would be 2 queens of spades within a 26-card selection, given that 26 constitutes twice the quantity of 13. Curiously, several of my acquaintances arrived at a similar conclusion.
 
Student108 said:
I request your assistance in discerning the flaw within my reasoning. The initial premise was centered on the observation that a queen of spades appears once within every 13-card subset. Consequently, the inference was drawn that there would be 2 queens of spades within a 26-card selection, given that 26 constitutes twice the quantity of 13. Curiously, several of my acquaintances arrived at a similar conclusion.
Click to expand...
It's a natural error; We tend to expect things to be proportional. But you have to think more deeply than that; the assumption is wrong.

How can you make a deck so that you can be sure that every set of 13 cards has at least one queen of spades? Keep thinking! (By the way, this has nothing to do with probability; it's about certainty!)

Once you figure that out, then you can answer the original question.
 
I will solve two of the cases I listed above.
Suppose 53 cards were the queen of spades. Then Freddy could have gotten how many queen of spades? In this case there is 1 card that is not a queen of spades.
If you pick 13 cards, then you can get that 1 non queen of spades and 12 queen of spades OR 13 queen of spades.


Suppose 52 cards were the queen of spades. Then Freddy could have gotten how many queens of spades? In this case there are two cards that are NOT queen of spades.
If you pick 13 cards you can get 2 non queen of spades and 11 queen of spades OR 1 non queen of spades and 12 queen of spades OR 13 queen of spades.

In the above examples you are guaranteed at least 12 queen of spades in the first example and at least 11 queen of spades in the 2nd example.
According to the problem you will get (at least) one queen of spades. Can you get exactly 1 queen of spades. If yes, then 1 is your answer. Otherwise, can you get exactly 2 queen of spade. If yes, then 2 is your answer. Otherwise, can you get exactly 3 queen of spades?....
 
Steven G said:
I will solve two of the cases I listed above.
Suppose 53 cards were the queen of spades. Then Freddy could have gotten how many queen of spades? In this case there is 1 card that is not a queen of spades.
If you pick 13 cards, then you can get that 1 non queen of spades and 12 queen of spades OR 13 queen of spades.


Suppose 52 cards were the queen of spades. Then Freddy could have gotten how many queens of spades? In this case there are two cards that are NOT queen of spades.
If you pick 13 cards you can get 2 non queen of spades and 11 queen of spades OR 1 non queen of spades and 12 queen of spades OR 13 queen of spades.

In the above examples you are guaranteed at least 12 queen of spades in the first example and at least 11 queen of spades in the 2nd example.
According to the problem you will get (at least) one queen of spades. Can you get exactly 1 queen of spades. If yes, then 1 is your answer. Otherwise, can you get exactly 2 queen of spade. If yes, then 2 is your answer. Otherwise, can you get exactly 3 queen of spades?....
Click to expand...
I'm confused. The question is about what Freddy can get when he chooses 26 cards. You're talking only about choosing 13. so you can't be getting the answer just from this thinking.

That's why I think you need to think in two steps. This is only the first.
Dr.Peterson said:
What is a "woreint"?
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By the way, I finally figured out what "woreint" means -- it's a typo for "wording", because e is near d, and t is near g, on the keyboard. This is why proofreading is important. So you don't understand the wording of the problem. I hope that's been cleared up.
 
Dr.Peterson said:
I'm confused. The question is about what Freddy can get when he chooses 26 cards. You're talking only about choosing 13. so you can't be getting the answer just from this thinking.

That's why I think you need to think in two steps. This is only the first.

By the way, I finally figured out what "woreint" means -- it's a typo for "wording", because e is near d, and t is near g, on the keyboard. This is why proofreading is important. So you don't understand the wording of the problem. I hope that's been cleared up.
Click to expand...
Sorry about that, I intended to say wording but was in a rush when typing this question. The wording of the problem is hard to approach, for 26 I understand what another mathematician stated about it being 14, which I agree. What do you think about the final answer?
 
Student108 said:
Sorry about that, I intended to say wording but was in a rush when typing this question. The wording of the problem is hard to approach, for 26 I understand what another mathematician stated about it being 14, which I agree. What do you think about the final answer?
Click to expand...
I agree about 14, but can you explain how to get this number?
 
Student108 said:
Sorry about that, I intended to say wording but was in a rush when typing this question.
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That's okay; I like puzzles. It would have been nice if you had responded sooner to our queries about that, though.
Student108 said:
The wording of the problem is hard to approach, for 26 I understand what another mathematician stated about it being 14, which I agree. What do you think about the final answer?
Click to expand...
The numerical answer isn't the important thing. I want to know whether you now understand the meaning of the question, and how to think about it. So, what do you think about it? (Not just yes or no, but why.)
 
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