The photograph shows the last Russian emperor, Nicholas II, his wife Alexandra, his four daughters (Olga, Tatiana, Maria and Anastasia) and his son Alexei, who was hemophiliac.

Let \( P = \dfrac{a}{b} \), for coprime positive integers \( a \) and \( b \), be the probability that only **two** of the couple's daughters carry the gene for hemophilia.

Evaluate \( a+b\).

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