Please help with veritas P & C example

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.

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!!

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.

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!!