The definition of inherent risk is the susceptibility of an assertion to a material misstatement, assuming that there are no related internal control structure policies or procedures. Complex calculations are subject to inherent risk just because they are complex and there are many opportunities for errors.
The definition of audit risk is the risk that the auditor may unknowingly fail to appropriately modify his or her opinion on financial statements that are materially misstated.
The definition of detection risk is the risk that the auditor will not detect a material misstatement that exists in an assertion.
The definition of sampling risk is the risk that a particular sample will not be representative of the entire population.
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