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Aptitude - Probability - Discussion

@ : Home > Aptitude > Probability > General Questions - Discussion

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"No one is as deaf as the man who will not listen."
- (Proverb)
9. 

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

[A].
1
15
[B].
25
57
[C].
35
256
[D].
1
221

Answer: Option B

Explanation:

Let S be the sample space.

Then, n(S) = 52C2 = (52 x 51) = 1326.
(2 x 1)

Let E = event of getting 2 kings out of 4.

n(E) = 4C2 = (4 x 3) = 6.
(2 x 1)

P(E) = n(E) = 6 = 1 .
n(S) 1326 221


Shyam said: (Wed, Jan 19, 2011 06:11:21 AM)    
 
How 2 kings out of 4 .?

Rahul said: (Tue, May 31, 2011 04:48:15 PM)    
 
Because in apack of cards 4 kings are there. So selecting 2 kings out of 4 is 4c2. Generally in apack of cards the 4 suits are aces, kings, queens, jacks.

Ajith Kumar said: (Tue, Jul 19, 2011 12:05:23 PM)    
 
@ Shyam

Generally there are only four kings in a pack of 52 cards.

Prince said: (Sun, Jul 24, 2011 07:24:45 PM)    
 
(52 x 51)
---------..? how is this equation possible..?
(2 x 1)

S.Mounica said: (Tue, Jul 26, 2011 10:16:39 AM)    
 
Its formula, nC2 = n*n-1/1*2

So we get it.

Arun Sharma said: (Fri, Aug 5, 2011 11:34:59 PM)    
 
I am really confused about this answer. I think the logic of 2 kings out of 4 is wrong. There are 13 types of cards in a pack and you are looking for the two cards that you are pulling out to be of one type.

So it should be (13x12)/(2x1) - this is the probability that the two cards you pull will be of one type. This will have to be divided by the sample space.

So it will be 156/2 = 78.

Hence 78/1376 = 39/692.

Swetha said: (Tue, Nov 8, 2011 03:36:51 PM)    
 
@Arun Sharma

There are 13 types of cards.,but the question asked is both are kings. We have only 4 kings. Therefore we must take 2 kings out of 4 kings.

Santhu said: (Tue, Jun 12, 2012 10:34:25 PM)    
 
Can anyone clarify my doubt?

In pack of card there are 4 kings once if we draw king then 4C1 then remaining kings are 3 2nd king we need to take from 3 so 3C1.

So answer is 4C1*3C1/52C2 is it correct?

Rohit said: (Sat, Feb 16, 2013 08:19:14 PM)    
 
4/52 is the chance of getting 1st King.
3/51 is the chance of getting 2nd King.

So, probability of getting 2 kings is:
4/52 * 3/51 = 1/221.

Lola said: (Wed, May 29, 2013 12:43:41 PM)    
 
The n(k) = 4, so the p(getting a king)=4c1, or 4/52 : p(getting 2 king) = 4c2. NB: combination mean selection.

Gaurav Garg said: (Tue, Jun 4, 2013 12:05:58 PM)    
 
@Santhu.

We are not selecting cards from only 4 kings, we are selecting them from all 52 cards And next time from 51 cards.

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