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# Aptitude - Probability - 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

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.