According to Atticus, what is the state prosecutor counting on to convince the jury to convict Tom Robinson in To Kill a Mockingbird?

I think that you are talking about what Atticus says in
Chapter 20 when he is delivering his closing argument to the jury.  He does not really
focus so much on the prosecutor as on the Ewells,
though.

What he says they are relying on is a prejudice
against blacks.  He says they are relying on the jury to believe that blacks are
completely immoral and not to be trusted.  He says that their testimony requires the
jury to believe that all black people lie all the time and that all black men want to
violate white women if only they could get the chance.