Two cards are drawn together from a pack of 52 cards. The probability that one is spade and other is king is ?

Question

I did it from conditional probability , first case when we pick one spade first and then pick king next

so it is equal to  ,probability of picking up a spade*probability of picking a  king given that we have already picked up a spade so it is equal to 13/52 * 1/51

And then probability of picking up a king and a spade =probability of picking up a king *probability of picking up a spade given that we have already picked up a king which is equal to 4/52 * 12/ 51

Now summing up both of these I get the answer 

=61 / 52*51 =0.023 

What is wrong in this method ?

Comments

Acc. to me

answer is (13c1*4c1)/(52c2)    -     1/52

= 53/(52*51)

Answer 1

13 spades

we need to select 2 cards having one spade and one king

here king can be spade also

{(12c1 * 1c1)(both the cards from spade) +(13c1 * 3c1)(king from another sets)} / 52c2

Answer 2

One (King (not spade)) other is Spade + One( king spade ) One more for Spade

(3C1*13C1 + 1*12C1)/52C2 =1/26

Comments

what is wrong in my approach ?

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sir here we are drwing 2 cards na if we get 1st card as spade king then what about second card ??

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I modified my approach , Now let 's say the first card I pick is a spade , Now the probability that the first card is a spade and the second card is a king = the probability of picking up a spade*probability of picking a king given that we have already picked up a spade =13/52*(4/51+3/51) , Here I am considering the case where the first card drawn which was spade was a king or it was not a king , if it was a king spade then I have remaining 3 choices for king and if it is not a king then I still have 4 choices for king .

Now the second case when the first card drawn is a king and the second card drawn is a king , so ,the probability of picking up a king and a spade =probability of picking up a king*probability of picking up a spade given that we have already picked up a king which is equal to 4/52*( 12/51+ 13/51) , since if a king was already drawn there may be a possibility that king was already a spade so now remaining choices for spade are 12 and if the king drawn was not a spade then remaining choices for spade are 13 .

Now If I sum up these two cases , what's wrong in this ?

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shivanisrivarshini, If we draw a card and get spade+ king at 1st then we can take it as a king or spade.so,

I) If it is a king then 2nd will be spade ->(1c1*12c1)

II) If it is a spade then 2nd will be king ->(13c1*3c1)