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# What is the probability of getting a King and a Queen in a single draw

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What is the probability of getting a King and a Queen in a single draw [#permalink]

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15 Jun 2011, 22:40
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25% (medium)

Question Stats:

55% (01:21) correct 45% (00:22) wrong based on 55 sessions

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What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?

A. 1/16

B. (4C1 * 4C1) / 52C2

C. 4/52 * 4/51

D. 8C2 / 52 C 2

E. (8 * 7) / 52C2
[Reveal] Spoiler: OA

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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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15 Jun 2011, 22:50
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Expert's post
soaringAlone wrote:
What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?

A. 1/16

B. (4C1 * 4C1) / 52C2

C. 4/52 * 4/51

D. 8C2 / 52 C 2

E. (8 * 7) / 52C2

Where are these questions from? Two things:

* the GMAT will *never* ask questions about standard decks of cards, since people who play bridge or poker would have a substantial (and unfair) advantage over people who do not;

* the GMAT will *never* use notation like '52C2' in an answer choice. That's not even a standard notation in general mathematics; it's more a convenient shorthand to use in internet forums. GMAT answer choices will always be written either as numbers, or using factorials

So that makes me wonder what the source is for these questions, and whether it contains a lot of other irrelevant material.

In any case, there are 4 Kings and 4 Queens in a standard deck. We need our first card to be one of these 8; there is an 8/52 probability our first card is from this group. Then when we pick the second card, we will be picking from 51 cards in total, and there will be 4 left which are of the type we need (if we picked a King first, we need one of the four Queens and vice versa), so there is a 4/51 probability the second card is the right type, and the answer is (8/52)(4/51).

That is equal to answer choice B, though you'd never see anything that looks like answer choice B on the GMAT. It's a bit absurd to write '4C1' in that answer choice anyway, since '4C1' is just equal to 4.
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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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15 Jun 2011, 23:19
its a B here.
4 suits hence 4c1 each for king and queen.
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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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27 Apr 2016, 06:53
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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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27 Apr 2016, 07:05
soaringAlone wrote:
What is the probability of getting a King and a Queen in a single draw of two cards from a pack of well-shuffled cards?

A. 1/16

B. (4C1 * 4C1) / 52C2

C. 4/52 * 4/51

D. 8C2 / 52 C 2

E. (8 * 7) / 52C2

Hi,
the MOST important point here is SINGLE draw..
this means there is NO order..

there are 4 kings, so we can choose a king in 4C1 way..
there are 4 Queens, so we can choose a Queen in 4C1 way..

total possible way = $$\frac{4C1*4C1}{52C2}$$
B
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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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28 Apr 2016, 03:55
Hey...
If I said .. There are 4 ways to pick a king and 4 ways to pick a queen ...
2 ways to pick the first card.. The I have the equation
2*(4/52)*(4/51)
... Is this correct

Posted from my mobile device
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Re: What is the probability of getting a King and a Queen in a single draw [#permalink]

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29 Apr 2016, 04:20
nikhiljd wrote:
Hey...
If I said .. There are 4 ways to pick a king and 4 ways to pick a queen ...
2 ways to pick the first card.. The I have the equation
2*(4/52)*(4/51)
... Is this correct

Posted from my mobile device

Hi,
the Q will not say two ways to pick the card But itwould say..
two cards are picked One after another INSTEAD of in a single draw
then it will be 4C1*4C1*2/52C1
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Re: What is the probability of getting a King and a Queen in a single draw   [#permalink] 29 Apr 2016, 04:20
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