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# probability Q

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Senior Manager
Joined: 07 Oct 2003
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31 May 2004, 13:24
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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) Â½
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31 May 2004, 14:51
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...
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31 May 2004, 15:43
Manager
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31 May 2004, 20:59
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
Senior Manager
Joined: 07 Oct 2003
Posts: 350
Location: Manhattan
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06 Jun 2004, 20:25
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!
06 Jun 2004, 20:25
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