Looks right to me.
So Ive done the question just not sure if it is right..
a hand of 13 cards is to be dealt at random and without replacement from an ordinary deck of playing cards. find the conditional probability that there are at least three kings in the hand given that the hand contains at least two kings.
proof:
ways of getting exactly 2 kings = 4c2*48c11 = A
ways of getting exactly 3 kings = 4c3*48c10 = B
ways of getting exactly 4 kings = 4c4*48c9 = C
ways of getting at least 3 kings = B+C
ways of getting at least 2 kings = A+B+C . [this is the sample space]
P[at least 3 kings | at least 2 kings]
= (B+C) / (A+B+C)
= 0.1704 IS this correct or no?