The break-even spread when some traders know the answer

A stock is worth either \100$or$$90$, each with probability$\tfrac12$; prior fair value is$$95$. A fraction$\alpha = 0.30$of the traders you face are **informed** (they already know the true value and trade accordingly); the other$70%$ are uninformed and buy or sell at random, fifty-fifty, regardless of value.

You must post a bid and an ask that earn zero expected profit per trade, the competitive spread.

Derive the break-even bid and ask.