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probability Q

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Senior Manager
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probability Q [#permalink] New post 31 May 2004, 12:24
This problem has been recently posted but I don't believe a clear solution was ever presented.

What is the probability that you receive a pair when you are dealt two cards from a complete deck?

a) 1/17
b) 1/13
c) 1/12
d) 4/17
e) ½
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 [#permalink] New post 31 May 2004, 13:51
i think answer is 26/52 =1/2
if the cards are picked together ...
if first one card is picked then the second the answer would be=1/52 *3/51
pls correct me if i m wrong...
what is the ifficial answer
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 [#permalink] New post 31 May 2004, 14:43
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 [#permalink] New post 31 May 2004, 19:59
Think of it like this.

Step 1:
What is the probability that first card is an ace
= 4/52
Step 2:
What is the probability that second card is also an ace (given that the first card already drawn was an ace)
=3/51

Hence the probability that I get a pair of aces when I draw two cards
= 4/52 * 3/51

Now we have 13 card numbers eg: Aces, Kings, Queens, Jacks ....

Therefore there are 13 ways in which I can perform step 1 and step 2 , asking questions like What is the probability I get a pair of kings when I draw two cards....
and the answer for each of these 13 steps = 4/52 * 3/51

Therefore total probability of having any pair when we draw two cards

= 13 * 4/52 * 3/51

= 1/17
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 [#permalink] New post 06 Jun 2004, 19:25
anupag wrote:
Think of it like this.

Step 1:
What is the probability that first card is an ace
= 4/52
Step 2:
What is the probability that second card is also an ace (given that the first card already drawn was an ace)
=3/51

Hence the probability that I get a pair of aces when I draw two cards
= 4/52 * 3/51

Now we have 13 card numbers eg: Aces, Kings, Queens, Jacks ....

Therefore there are 13 ways in which I can perform step 1 and step 2 , asking questions like What is the probability I get a pair of kings when I draw two cards....
and the answer for each of these 13 steps = 4/52 * 3/51

Therefore total probability of having any pair when we draw two cards

= 13 * 4/52 * 3/51

= 1/17


thanks for such clear explanation!
  [#permalink] 06 Jun 2004, 19:25
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