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Please help with veritas P & C example

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Please help with veritas P & C example

by sachin_yadav » Sat Dec 11, 2010 11:25 pm
What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards (52 cards with 13 sets of 4 matching cards) ?


My take was:- 52/52 * 1/51 = 1/51. The question is talking about pairs and asking to pick top two cards, so i believe the pair is of two cards; however this is wrong. The explanation says, this question is asking for the probability to get ANY pair, not one specific pair (say a pair of 2s or 3s). Therefore the probability to get any pair picking the top two cards off the deck is

52/52 * 3/51 = 3/51


Is it a pair of 2 or more ? Please clarify this doubt.
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by kvcpk » Sat Dec 11, 2010 11:55 pm
sachin_yadav wrote:What is the probability that you get a pair when picking the top two cards off of a randomly shuffled deck of cards (52 cards with 13 sets of 4 matching cards) ?


My take was:- 52/52 * 1/51 = 1/51. The question is talking about pairs and asking to pick top two cards, so i believe the pair is of two cards; however this is wrong. The explanation says, this question is asking for the probability to get ANY pair, not one specific pair (say a pair of 2s or 3s). Therefore the probability to get any pair picking the top two cards off the deck is

52/52 * 3/51 = 3/51


Is it a pair of 2 or more ? Please clarify this doubt.
Hi Sachin,

In my explanation, I assume u know cards - symbols.
Let us say we picked K (King-Spade) in the first card.
Now, to get a pair, we can pick up any of these three:
K (King - Clubs)
K (King - Diamonds)
K (King - Hearts)

Hence out of the remaining 51 cards, we have 3 positive scenarios.
Hence probability is 3/51

Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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by sachin_yadav » Sun Dec 12, 2010 8:12 pm
kvcpk wrote:
Hi Sachin,

In my explanation, I assume u know cards - symbols.
Let us say we picked K (King-Spade) in the first card.
Now, to get a pair, we can pick up any of these three:
K (King - Clubs)
K (King - Diamonds)
K (King - Hearts)

Hence out of the remaining 51 cards, we have 3 positive scenarios.
Hence probability is 3/51

Hope this helps!!
Thanks kvcpk for your reply.

Okay there are 52 cards, i pick one card(king-spade), now to make it a pair i can select 3 cards from the remaining 51 cards . But again there is still one confusion, is it a pair of 2 or 3 ?

What if the question is asking for a pair of 3 ?

So, it will be 52/52 * 2/51. I am not sure.

Waiting for your reply

Please anyone who can tell me the crux of this problem.
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by kvcpk » Sun Dec 12, 2010 9:44 pm
sachin_yadav wrote: Thanks kvcpk for your reply.

Okay there are 52 cards, i pick one card(king-spade), now to make it a pair i can select 3 cards from the remaining 51 cards . But again there is still one confusion, is it a pair of 2 or 3 ?

What if the question is asking for a pair of 3 ?

So, it will be 52/52 * 2/51. I am not sure.

Waiting for your reply

Please anyone who can tell me the crux of this problem.
Couple of things here:
Pair is always 2.
Question specifically mentions "when picking the top two cards off"
Hence we are only looking for a pair of cards which have the same value.

Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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by sachin_yadav » Mon Dec 13, 2010 12:54 am
kvcpk wrote: Couple of things here:
Pair is always 2.
Question specifically mentions "when picking the top two cards off"
Hence we are only looking for a pair of cards which have the same value.

Hope this helps!!

Thanks once again...
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