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# From an ordinary deck of cards, only 12 picture cards are

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From an ordinary deck of cards, only 12 picture cards are [#permalink]

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19 Apr 2006, 15:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random. He then announce one of these cards is the King or Spades. What is the probability that he holds two Kings? (hint: list the possible sample space carefully).
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19 Apr 2006, 17:08
Consider the table below (I am not good at cards)
King............1............1..................1.......................1
Queen.........2............2..................2.......................2
Jack............3............3..................3.......................3

In the 12 picture cards, We have a spade and a king (and it could be a spade king too).

Spade (Non King) X Any (Non Spade Non King)= 2 x 6 = 12
King (Non Spade) x Any (Non King Non Spade) = 3 x 6 = 18
Spade King x (Any Non Spade Non King) = 1 x 6 = 6
Thus total sample size is 45.
Out of this, Two kings are C(4, 2) = 12.
Thus probability = 12/45 = 4/15.
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19 Apr 2006, 17:20
Is it 1/35? I used conditional probability and got this value...
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19 Apr 2006, 20:31
Nope, this is not the answer.
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19 Apr 2006, 21:36
vipin7um wrote:
From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random. He then announce one of these cards is the King or Spades. What is the probability that he holds two Kings? (hint: list the possible sample space carefully).

2/17
if yes I'll explain
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20 Apr 2006, 09:13
Alright vipin, my last try...
Is it 2/7?

Knowing that it is a King or Spade we have 3 sets of possibilities for the 2 cards:
1. (King, Spade) = 4+4+4+3 = 15
3. (King, King) = 6

K of spade is part of all three of thse possibilities.
Number of overlaps in #2 and #3 is exactly 3*2 =6

Total = 15+6+6-3*2 = 21

2 kings can occur in 4C2 = 6 ways
Hence P(2 Kings) = 6/21 = 2/7
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20 Apr 2006, 09:26
I think it is not that hard. Since the player have announced that the first
card is a king we should not account for it is not. So the probability
that the player has two kings is a probability that the second card is a king. And this leaves us with 3/11.

What is OA ?
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20 Apr 2006, 09:55
3/11??
there are 4 kings in the 12 cards. if he has one, that leaves 3 out of the 11 remaining cards...
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20 Apr 2006, 12:49
4c1/12c1 * 3c1/11c1
1/11 ?
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20 Apr 2006, 13:54
deowl wrote:
I think it is not that hard. Since the player have announced that the first
card is a king we should not account for it is not. So the probability
that the player has two kings is a probability that the second card is a king. And this leaves us with 3/11.

What is OA ?

OA is 3/11. And the official explanation is same as above only. But I am also not fully convinced by OE.

Because one of the card can be either a king or a spade or both. Note that amongst the 12 picture cards, there are 4 kings and 3 spades. But the 3 spades also include the spades King.

So one of the two cards probability to be king is 4/6. And the other card's probability is 3/11.

=> 4/6 * 3/11 * 2C1 = 4/11.

Pls feel free to discuss this more.

Thanks,
Viipin
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20 Apr 2006, 14:01
Quote:
He then announce one of these cards is the King or Spades

The first card has to be a king or a spade. So probability for a king is 1/2

The second card has to be a king out of the remaining 3 kings. Means the probability is 3c1/11c1

So the answer is (1/2) x (3/11) = 3/22

is that correct
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20 Apr 2006, 16:07
vipin7um wrote:
From an ordinary deck of cards, only 12 picture cards are retained. They are shuffled (mixed) and a man draws 2 cards at random. He then announce one of these cards is the King or Spades. What is the probability that he holds two Kings? (hint: list the possible sample space carefully).

It should be King "of" spades....i think there is a typo in the question
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20 Apr 2006, 20:35
vipin7um wrote:
deowl wrote:
I think it is not that hard. Since the player have announced that the first
card is a king we should not account for it is not. So the probability
that the player has two kings is a probability that the second card is a king. And this leaves us with 3/11.

What is OA ?

OA is 3/11. And the official explanation is same as above only. But I am also not fully convinced by OE.

Because one of the card can be either a king or a spade or both. Note that amongst the 12 picture cards, there are 4 kings and 3 spades. But the 3 spades also include the spades King.

So one of the two cards probability to be king is 4/6. And the other card's probability is 3/11.

=> 4/6 * 3/11 * 2C1 = 4/11.

Pls feel free to discuss this more.

Thanks,
Viipin

Vipin, IMHO if you give us the OE as Deowl explained (he explained as if the one of the card is the King of Spades, but it's not stated in the question) there is a typo in the question in third sentence. "... He then announce one of these cards is the King OR Spades..."
Accrding to you and to Deowl there must be 'OF'

Am I right?

In any case let's discuss it further from the point that he one of the card is the King OR Spades.
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20 Apr 2006, 21:38
M8 wrote:
vipin7um wrote:
deowl wrote:
I think it is not that hard. Since the player have announced that the first
card is a king we should not account for it is not. So the probability
that the player has two kings is a probability that the second card is a king. And this leaves us with 3/11.

What is OA ?

OA is 3/11. And the official explanation is same as above only. But I am also not fully convinced by OE.

Because one of the card can be either a king or a spade or both. Note that amongst the 12 picture cards, there are 4 kings and 3 spades. But the 3 spades also include the spades King.

So one of the two cards probability to be king is 4/6. And the other card's probability is 3/11.

=> 4/6 * 3/11 * 2C1 = 4/11.

Pls feel free to discuss this more.

Thanks,
Viipin

Vipin, IMHO if you give us the OE as Deowl explained (he explained as if the one of the card is the King of Spades, but it's not stated in the question) there is a typo in the question in third sentence. "... He then announce one of these cards is the King OR Spades..."
Accrding to you and to Deowl there must be 'OF'

Am I right?

In any case let's discuss it further from the point that he one of the card is the King OR Spades.

Hi M8,
Actually, I didn't even realize that the original question had a typo untill Shevy mentioned it.
I think it has become a little confusing. I will try to sort things out here.

Case1: The man anounced that one of the cards is a king OF spades.

Off. Answer to case1 is 3/11.
Since we already know that one of the cards is a king, the other card can be chosen out of the remaining 3 king cards. so the probability is -

3 / 11.

Case2: The man anounced that one of the cards is a king OR spades.

No OA answer for this since this was not the original problem. My answer to this would be 4/11.

Since, one of the card can be either a king or a spade or both. Note that amongst the 12 picture cards, there are 4 kings and 3 spades. But the 3 spades also include the King of Spades.

So one of the two cards probability to be king is 4/6.

And the other card's probability is 3/11.

=> 2C1 * 4/6 * 3/11 = 4/11.

HTH...
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20 Apr 2006, 21:43
M8

You are right. Indeed I have read this question as "king of spades". Othervise the answer would be 4/6 * 3/11 = 2/11 of cause.

Last edited by deowl on 21 Apr 2006, 15:47, edited 1 time in total.
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21 Apr 2006, 12:25
Vipin what is the source of your question?
21 Apr 2006, 12:25
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