Let P (E) = Prabability of getting a spade
P(Q) = Probability of getting a red queen
Hence required probability is $P (E_1) P(\frac{Q_2}{E_1}) + P (Q_1)P(\frac {E_2}{Q_1})$
$=\frac{13C_1}{52 C_1} \times \frac{2C_1}{51C_1} + \frac{2C_1}{52C_1} \times \frac{13 C_1}{51 C_1}$
$=2 (\frac{13}{52} \times \frac{2}{51})$
$= \frac{1}{51}$