Probability
Aptitude

 Back to Questions
Q.

Four cards are drawn at random from a pack of 52 plating cards. Find the probability of getting all the four cards of the same suit.

 A.

13/270725

 B.

91/190

 C.

178/20825

 D.

44/4165

 Hide Ans

Solution:
Option(D) is correct

Four cards can be selected from 52 cards in ${^{52}C_4}$ ways.

Now, there are four suits, e.g. club, spade, heart and diamond each of 13 cards.

So total number of ways of getting all the four cards of the same suit:

$⇒ {^{13}C_4} + {^{13}C_4} + {^{13}C_4} + {^{13}C_4}$

$= 4 × {^{13}C_4}$

So required probability,

$= \dfrac{4 × {^{13}C_4}}{^{52}C_4}$

$= \textbf{44/4165}$

Edit: Final answer has been changed from 198/20825 to 44/4165, after recieving a comment from Saurabh Bansal.


(7) Comment(s)


Gau
 ()

what is the meaning of C4????



Saurabh Bansal
 ()

The final computation is wrong.

It should be,

$\dfrac{4 \times ^{13}C_4}{^{52}C_4}=\dfrac{44}{4165}$


Deepak
 ()

Thank you Saurabh for letting me know, corrected the mistake.


Btm
 ()

The solution is correct but the answer they provide is wrong (maybe a calculation error).

using software (R):

4 * choose(13, 4)/ choose(52, 4) = 44 /4165 or 132/12495



Steve
 ()

I keep comming up with $4C1*13C4/52C4$ to be $220/20825$ which is exactly the same as subodh and danh



Subodh
 ()

Answer is

$(4\times 13C4)/(52C4) = 132/12495 = 44/4165$



Danh
 ()

The correct probability is 4 times the probability of four cards of one suit, which is four times $13/52 * 12/51 * 11/50 * 10/49$.

So, the correct answer is,

$= 4 * 13/52 * 12/51 * 11/50 * 10/49$

$= 12 * 11 / 51 / 49 / 5$

$= (12 * 11) / (51 * 49 * 5)$

$= 132/12495$.

Mohammed Javad is correct.