There are 2 red queens (hearts and diamonds) in a standard deck of cardsso the probability of drawing a red queen is:

\(\displaystyle\frac{{2}}{{52}}=\frac{{1}}{{26}}\)

Since there is no replacement, there remains a total of \(13 + 12 = 25\) red cards out of the remaining 51 cards so the probability that the next crad drawn is a red card is:

\(\displaystyle\frac{{25}}{{51}}\)

Hence, the probability of getting a red queen and then another red card is the product of the probabilities:

\(\displaystyle\frac{{1}}{{26}}\cdot\frac{{25}}{{51}}=\frac{{25}}{{1326}}\)