= Solution
Assume Alice independently chooses X or Z with equal <probabilities> and that bit labels $0,1$ identify the corresponding positive and negative <eigenstates>. If Daisy measures Z, she reads a Z-encoded bit correctly with <probability> one and an X-encoded bit correctly with <probability> one half. Therefore
$$
\boxed{P(\text{correct bit}\mid M_Z)=\frac12\cdot1+\frac12\cdot\frac12=\frac34.}
$$
The <probability> to read the entire independently encoded $n$-bit check number correctly by this strategy is $(3/4)^n$.
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