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The unit and item nonresponse distinction matters: embarrassment was not recorded for the 300 unit nonresponders. Conditional independence of unit response and virginity given embarrassment is therefore not enough unless the embarrassment distribution among unit nonresponders is also supplied.

One sufficient set of additional assumptions is that unit response is independent of the pair consisting of embarrassment and virginity. Equivalently for this estimation purpose, assume that unit nonresponders have the same embarrassment mixture as the other 750 individuals, and the same virginity probabilities within those strata. The former gives an embarrassed fraction $300/750=0.4$, and the latter gives probabilities $0.18$ and $0.08$. Their estimated positive proportion is consequently $0.4(0.18)+0.6(0.08)=0.12$, or 36 of the 300. Combining the groups givesThe item-response assumption from (ii) supplies the first 90; the added unit-response transport assumptions supply the final 36. A weaker sufficient assumption is simply that the unit nonresponders' marginal virginity proportion equals the estimated $12\%$ in the other group, but it is still untestable from these data.

Without any unit-response transport assumption, retain the item assumption and write the unidentified unit proportion as $p_U$. ThenThus the extrapolation is an assumption-dependent estimate, not a quantity determined by the observed table alone.