Final answer:
Propofol is contraindicated for patients with an egg allergy as it may contain egg lecithin. Thiopentone, midazolam, and ketamine do not contain egg products and are not contraindicated for such allergies.
Step-by-step explanation:
The induction anaesthetic that is contraindicated in a patient allergic to eggs is Propofol. Propofol is an intravenous drug widely used for the induction of anesthesia but can contain egg lecithin as an emulsifier. Patients with an egg allergy may be at risk of a hypersensitivity reaction to Propofol.
Other options listed, such as thiopentone (another barbiturate), midazolam (a benzodiazepine), and ketamine do not contain egg products and are not contraindicated due to an egg allergy. It's essential for healthcare providers to screen for allergies before administering anesthesia and to be prepared with alternatives and emergency protocols in the event of an allergic reaction.