Win on primes, lose half on composites from 2 to 10

An integer $n$ is drawn uniformly from $\{2,3,\dots,10\}$. If $n$ is prime you win $n$ dollars; if $n$ is composite you lose $n/2$ dollars. What is the most you should pay to play? Answer $0$ if you would decline to play.

$0$. The primes $2,3,5,7$ contribute $+17$ and the composites $4,6,8,9,10$ contribute $-18.5$, so the expected value is $\tfrac{17-18.5}{9}=-\tfrac16$ dollar. A game with negative expectation is not worth any entry fee, so you should not play.