Question

using a deck of cards,what is the probability that you would pull a red kind and a black queen in two pulls without replacing the first card back into the deck?

Answer 1

I believe you mean read KING, not red KIND. There are two red kings and two black queens. The probability of drawing either one, in a single draw, is 2/52 = 1/26.
There are two ways you could end up with one black queen and one red king: You could get the king first or the queen first. The total probability is
2*(1/26)^2 = 1/338

Answer 2

Since you are not replacing the card, the prob of the second draw is different from the first draw.

could be RK,BQ or BW,RK
prob of that is (2/52)(2/51) + (2/52)(2/51)
= 2(2/52)(2/51) = 2/663

or

choose a red king -->C(4,2) = 2
choose a black queen --> C(4,2) = 2
choose any two cards --> C(52,2) = 1326
prob = 2*2/1326 = 2/663

Answer 3

Reiny is correct; I missed the word "without" (replacing).