Mostly confused on how to find the sum of "at least" 5.

Question

Suppose you randomly draw two cards from a standard deck and roll a pair of dice. Determine the probability that you draw 2 black cards and roll a sum of at least 5. 

Answer 1

The sum is at least 5, that mean could be p(5,6,7,8,9,10,11,12), or 1-p(2,3,4). Let 's do probability of getting 2,3,4

for 2: 1+1

for 3:1+2, or 2+1

for 4: 1+3,3+1, 2+2,

6 possible combinations out of 36 total 

so p(sum>=5)=1-6/36=5/6

draw two black cards out of 52 cards is 26/52=1/2

so the overall probability is 1/2*5/6=5/12