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# Stats question watch

1. I have six decks of cards, all fully shuffled so the order is completely random.
I draw two cards.
What is the probability they are exactly the same card? (e.g 2 King of Clubs or 2 Jack of Hearts)

Thanks
2. Anyone?
3. Sorry I also read the question wrong haha....it's jsut 5/311.

4. EDIT:

Oh, didn't read properly, six decks. Wait a while

Should be correct (I hope)

EDIT:

Aaah, again misread. Thought same card in meaning of ace or 4, but doesn't matter whether it's diamonds/hearts etc. Oh wells, the poster below is correct
5. (1 / 52) * ( 5 / 311) = 5 / 16172
6. I disagree with the answers so far.

I believe the question is 'what is the probability that the second card you draw matches the first?'

There are 6*52 cards altogether. Once the first card is drawn only five copies of that card remain.
7. 5/311.

6 decks of 52 cards per deck = 312 cards.
you've taken one so there's 311 left.
and only 5 of the card remain.

so it's 0.016 or 5/311
8. The total number of (ordered) possible hands is .

Now we restrict our potential hands to those which consist of two of the same card.

There are ways of choosing the first card, and then only ways of choosing the second card. This gives a total of hands which have both the same card.

Thus the probability of drawing two cards out of the deck which are the same is which, of course, agrees with Gemma's answer above.
9. Thanks all you good people!

Another one.
Same set up, 6 decks, two cards are randomly drawn.

What is the probability that they are the same number and the same colour? E.g King of Heart, King of Diamonds, or 7 of clubs, 7 of spades.
Lastly, what is the probability they are the same number, but not same suit or colour?, e.g King of Diamonds, King of Clubs, or 7 of Hearts, 7 of spades?
10. As before, it doesn't matter what the first card is.

In first case, of the 311 cards that then remain, 11 cards will count, five copies of the original, plus 6 copies of its partner (KH - KD)

11/311

For the last bit 6 copies of each of two suitable cards are available. (If KH drawn first, then KC or KS will do)

So 12/311

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