Originally Posted by
Wilmer Quite different if 1 deck, and sum to be even; like:
"You randomly draw 2 cards from a standard deck of 52.
What's the probability that the sum of the 2 cards is 8?"
1st card: 28/52 = 7/13
2nd card: (6/7)(4/51) + (1/7)(3/51) = 9/119
Probability: (7/13)(9/119) = 9/221
Agree?
Agreed; and just to be clear, that's drawing two cards from a single deck without replacement where aces count as 1.
Brute force check in PARI/GP
Code:
Input: s=0;for(i=0,50,for(j=i+1,51,if(i%13+1+j%13+1==8,s++)));s
Output: 54
Input: 54/binomial(52,2)
Output: 9/221