Two cards are drawn successively from a deck of 52 cards. What is the

Question

Two cards are drawn successively from a deck of 52 cards. What is the probability that the second card is higher in rank than the first card?

A. 1/17
B. 7/17
C. 1/2
D. 8/17
E. 9/17

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chetan2u · Accepted Answer

There are a total of 52 cards. Now the first can be any of the 52, so the probability is 52/52=1.
In the remaining cards, the possibility of same rank is 3, so probability of same rank = 3/51.

Thus the probability of different rank =  \frac{51-3}{51}=\frac{48}{51}=\frac{16}{17} .
As the cards are not biased, the probability of higher rank will be the same as the probability of lower rank =>  \frac{1}{2}*\frac{16}{17} =\frac{8}{17}

D

Note
Probability of same rank =  \frac{1}{17} 
Probability of higher rank =  \frac{8}{17} 
Probability of lower rank =  \frac{8}{17} 
Total =  \frac{8}{17} + \frac{8}{17} + \frac{1}{17} = \frac{17}{17}

CrackverbalGMAT · Answer

SOLUTION:

The probability that the second card has the same face value as the first (Implying they both have the same face value) is 3/51, 
(As irrespective of what value the first card has, there will be exactly three cards left in the pile of 51 cards, that have that same value.

Probability that the two cards have different values is 1−3/51=48/51=16/17.

Clearly, the chance that the first card has a higher value than the second card is the same as the chance that the second card has a higher value than the first.

So each of them must be (1/2)*16/17 = 8/17 Hence    Option (D)

Hope this helps
  Devmitra Sen(Math)

CelestialBro · Answer

there are a total of 52 cards we start with the lowest value and go up till ace
2 3 4 5 6 7 8 9 10 J Q K A

P(picking first number)=4/52 and 
P(picking second number) is what is tricky here.

Say after we pick 4, there are 5 6 7 8 9 10 J Q K A value cards bigger than 4 which is 40 cards from the deck which are bigger than 4s.
this can be constructed for all the value cards:

P(2 and higher)= 4/52 * 48/51
P(3 and higher)= 4/52 * 44/51
P(4 and higher)= 4/52 * 40/51 and so on...

the final probability of (A number and a higher number)=P(2 and higher)+P(3 and higher)+ P(4 and higher) + .... P(Ace and higher)
=> (4 / 52 * 51) * (48+44+40+36....4 +0)= (4 / 52*51) * 312 = 8/17

Two cards are drawn successively from a deck of 52 cards. What is the

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