Break-even ask

A contract is worth $80$ or $20$ with equal probability. Each arriving trader is informed with probability $0.4$, in which case the trader buys when the value is $80$ and sells when it is $20$. Otherwise the trader is uninformed and buys or sells with probability $0.5$ each. The market maker sets the ask so that the expected profit on a buy order is exactly zero. What is the ask?

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