= Solution
Use the assumed 30% risk reduction for recipients and one-to-one transfers to distinct participants in the equal-sized opposite arm. Receipt fractions become 80% under intervention assignment and 20% under control assignment. Thus
$$
p_I^{\rm assignment}=0.8(0.0035)+0.2(0.005)=0.0038,\qquad p_C^{\rm assignment}=0.2(0.0035)+0.8(0.005)=0.0047.
$$
For 30,000 participants per arm, the expected counts are
$$
\boxed{\text{(i) intervention assignment: }114;\qquad\text{(ii) control assignment: }141.}
$$
The original benefit $1.5$ per thousand becomes $0.9$ per thousand: <symmetric treatment crossover attenuates a risk difference> by $1-2(0.2)=0.6$. Expected counts still sum to 255, since intact transfers preserve the total number of recipients. These predictions assume unchanged receipt-specific risks and distinct control recipients. Loss, sharing or repeated transfers would require a different receipt model.
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