What is the passive voice of you hope to win the prize?

He may win the prize = an active sentence - Subject + verb + object

Passive is formed by be + past aprticiple.

The past participle of win is won. So the the passive verb phrase is be won but the auxilarry verb may must be included so the full passive phrase is:

may be won.

In passive sentences the object goes before the verb = the prize may be won. If you want to say who or what does the action then add by + noun ( noun phrase) at the end of the sentence.

The prize may be won by him.