Exercise 2.27

Let $G$ be the event that the suspect is guilty. Let $T$ be the event that one of the criminals has blood type $1$ and the other has blood type $2$.

Thus,

For $P(G|T)$ to be larger than $p$, $p_1$ has to be smaller than $\frac{1}{2}$. This result makes sense, since if $p_1=\frac{1}{2}$, then half of the population has blood type $1$, and finding it at the crime scene gives us no information as to whether the suspect is guilty.