Step 1:

The number of queens in the pack of cards =4

Let $X$ be the discrete RV denoting the number of queens when two cards are drawn with out replacement .$X$ takes the values $0,1,2$

Step 2:

$P(X=0)$=probability of no queen being drawn

$\qquad\quad\;=\large\frac{48C_2}{52C_2}$

$\qquad\quad\;=\large\frac{48\times 47/1\times 2}{52\times 51/1\times 2}$

$\qquad\quad\;=\large\frac{564}{663}$

$P(X=1)$=probability that 1 card is a queen

$\qquad\quad\;=\large\frac{48C_1\times 4C_1}{52C_2}$

$\qquad\quad\;=\large\frac{48\times 4}{52\times 51/1\times 2}$

$\qquad\quad\;=\large\frac{96}{663}$

$\qquad\quad\;=\large\frac{32}{221}$

$P(X=2)$=probability that both cards are queens

$\qquad\quad\;=\large\frac{4C_2}{52C_2}$

$\qquad\quad\;=\large\frac{4\times 3/1\times 2}{52\times 51/1\times 2}$

$\qquad\quad\;=\large\frac{3}{663}$

$\qquad\quad\;=\large\frac{1}{221}$

Step 3:

The probability distribution is given by