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Electrophilic Addition:
Dilute sulfuric acid acts as a source of hydronium ions ($$\text{H}_3\text{O}^\oplus$$). The electron-rich carbon-carbon double bonds ($$\text{C=C}$$) undergo electrophilic addition by attacking the protons ($$\text{H}^\oplus$$).
Carbocation Stability (Markovnikov's Rule):
Protonation occurs selectively to form the more stable tertiary ($$3^\circ$$) carbocations rather than less stable secondary carbocations at both alkene sites.
Nucleophilic Attack by Water:
Water molecules ($$\text{H}_2\text{O}$$) present in the dilute medium act as nucleophiles, attacking both of the tertiary carbocations. After deprotonation, hydroxyl ($$-\text{OH}$$) groups are successfully attached to those positions.
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