In the hypothetical you gave, the unvaccinated is more likely (1/10 versus 1/100).
Compare that to the data from the UK vaccine surveillance report, and you'll see the opposite is true in reality (for age ranges 30-39 and above).
For example, for age range 30-39, between week 38 and 41 2021, there were 956.7 cases reported per 100,000 among the vaccinated, and 751.1 per 100,000 among the unvaccinated.
Compare that to the data from the UK vaccine surveillance report, and you'll see the opposite is true in reality (for age ranges 30-39 and above).
For example, for age range 30-39, between week 38 and 41 2021, there were 956.7 cases reported per 100,000 among the vaccinated, and 751.1 per 100,000 among the unvaccinated.