Latest CSC Aptitude Question SOLUTION: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?

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Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?

Asked In CSC kanika (11 years ago)

Unsolved Read Solution (11)

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gnanaprakash  (11 years ago)

2 cards drawn from 52 cards,so chances are 52C2
chances for drawing both black cards=26C2
chances for drawing both queen=4C2
so we will be having 2 queens in black cards,thus it is 2C2 which is 1
probability=(325+6-1)/1326=55/221

Is this solution Helpfull? Yes (42) | No   

Ankit agarwal  (11 years ago)

in a pack of 52 cards, we have 26 black cards in which there are two queens included. We have two more red queens that makes a total of 4 queens. Now favourable cases are (26C2 + 4C2) and total possible no. of cases in which 2 cards can be drawn are 52C2.
hence required probability = (26C2 + 4C2)/52C2

Is this solution Helpfull? Yes (9) | No (13)  

chanti  (9 years ago)

meghana if u dont mind could u please stop posting ur answers

Is this solution Helpfull? Yes (7) | No (2)  

amit singh  (11 years ago)

the probability for both cards are black= 26/52*25/51
the two black queens are considered in previous case
therefore the another probability is only for two red queens =2/52*1/51
the total probability= 26/52*25/51 + 2/52*1/51 =163/663

Is this solution Helpfull? Yes (4) | No (9)  

Sujay  (10 years ago)

We have n(s)=52c2=(52*51)/(2*1)=1326.
Let A=event of getting both black cards
B=event of getting both queens
A&B=event of getting queen of black cards
n(A)=26c2=(26*25)/(2*1)=325,
n(B)=4c2=(4*3)/(2*1)=6 and
n(A&B)=2c2=1
P(A)=n(A)/n(S)=325/1326;
P(B)=n(B)/n(S)=6/1326 and
P(A&B)=n(A&B)/n(S)=1/1326
P(AUB)=P(A)+P(B)-P(A&B)=(325+6-1/1326)=330/1326=55/221

Is this solution Helpfull? Yes (3) | No (1)  

ankita sharma  (11 years ago)

the answer is 331/1326

Is this solution Helpfull? Yes (2) | No (8)  

harika  (11 years ago)

probability for
both cards are black => 26/52*25/51 = 25/102

Is this solution Helpfull? Yes (2) | No (11)  

meghana  (11 years ago)

30-2=18/52

Is this solution Helpfull? Yes (1) | No (17)  

karuna parmar  (8 years ago)

26C2+4C2/52C2=331/1326

Is this solution Helpfull? Yes (1) | No (1)  

sunil  (9 years ago)

((2652)*(25/51))+((4/52)*(3/51))

Is this solution Helpfull? Yes | No (1)  

nandini   (8 years ago)

Ans. 26/52*25/51+ 4/52*3/51-2/52

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