Your statement is essentially "given OPs current state and prior probability of him making a mistake on the job, and the action of taking modafinil, that probability increases given the OP takes that action.
Which is not an accurate statement.
Modafinil is a nootropic, which means that it can increase attention, therefore decreasing the chance of a mistake. The probability that someone will experience more wakefulness and attention is high in this regard.
And it being FDA approved lowers the probability of an adverse reaction that can cause someone to not be in the right mind and make mistakes to a very small number, which accounts for things like heart conditions.
Which is not an accurate statement.
Modafinil is a nootropic, which means that it can increase attention, therefore decreasing the chance of a mistake. The probability that someone will experience more wakefulness and attention is high in this regard.
And it being FDA approved lowers the probability of an adverse reaction that can cause someone to not be in the right mind and make mistakes to a very small number, which accounts for things like heart conditions.