= Solution
In both cases the <alkene> undergoes concerted <oxygen> transfer from <metachloroperbenzoic acid>. The <alkene> <pi bond> forms one C–O bond to the terminal <peroxide> <oxygen>; <electron> redistribution forms the second C–O bond, breaks O–O, and transfers the peracid <proton> to its <carbonyl> <oxygen> as the <carboxylic acid> <product (chemistry)> forms. This cyclic <epoxidation> pathway delivers both C–O bonds from one face, without a freely rotating <carbon> intermediate.
For 1-methylcyclohexene, the two <alkene> faces are <enantiotopic>. Attack from opposite faces gives the two mirror-related <epoxides>, and an <achiral> peracid in an <achiral> environment cannot distinguish their <Gibbs energies of activation>. \b[The <product (chemistry)> is racemic, 1:1.]
For the cis-fused bicyclic <alkene>, the junction configuration and its puckered ring <conformation> make approach from the two faces sterically different. The folded saturated ring shields the concave face; <oxygen> transfer preferentially approaches the more exposed convex face, directed away from that ring. The alternative attack places the incoming peracid closer to the folded skeleton. \b[The 95:5 ratio represents facial <diastereoselectivity>], while concerted syn <oxygen> delivery is retained for either <product (chemistry)>. It should not be explained by free rotation or by one <epoxide> subsequently changing configuration. For scale only, if this ratio were measured under irreversible kinetic conditions at 298 K, it would correspond to $RT\ln(95/5)\simeq7.30\ \mathrm{kJ\,mol^{-1}}$ difference between the competing <Gibbs energies of activation>; the exam does not specify that <temperature>.
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