diff --git a/qiskit/primitives/backend_estimator.py b/qiskit/primitives/backend_estimator.py
index 02af7a619fef..9b14dbdc6408 100644
--- a/qiskit/primitives/backend_estimator.py
+++ b/qiskit/primitives/backend_estimator.py
@@ -39,7 +39,7 @@ def _run_circuits(
     circuits: QuantumCircuit | list[QuantumCircuit],
     backend: BackendV1 | BackendV2,
     **run_options,
-) -> tuple[Result, list[dict]]:
+) -> tuple[list[Result], list[dict]]:
     """Remove metadata of circuits and run the circuits on a backend.
     Args:
         circuits: The circuits
@@ -70,7 +70,7 @@ def _run_circuits(
     return result, metadata
 
 
-def _prepare_counts(results):
+def _prepare_counts(results: Sequence[Result]):
     counts = []
     for res in results:
         count = res.get_counts()
@@ -351,7 +351,7 @@ def _preprocessing(self) -> list[tuple[QuantumCircuit, list[QuantumCircuit]]]:
         return preprocessed_circuits
 
     def _postprocessing(
-        self, result: Result, accum: list[int], metadata: list[dict]
+        self, result: Sequence[Result], accum: list[int], metadata: list[dict]
     ) -> EstimatorResult:
         """
         Postprocessing for evaluation of expectation value using pauli rotation gates.
diff --git a/qiskit/primitives/backend_sampler.py b/qiskit/primitives/backend_sampler.py
index 932d7a52bd26..3976ff967c1e 100644
--- a/qiskit/primitives/backend_sampler.py
+++ b/qiskit/primitives/backend_sampler.py
@@ -158,7 +158,9 @@ def _call(
         result, _metadata = _run_circuits(bound_circuits, self._backend, **run_options)
         return self._postprocessing(result, bound_circuits)
 
-    def _postprocessing(self, result: Result, circuits: list[QuantumCircuit]) -> SamplerResult:
+    def _postprocessing(
+        self, result: Sequence[Result], circuits: list[QuantumCircuit]
+    ) -> SamplerResult:
         counts = _prepare_counts(result)
         shots = sum(counts[0].values())
 
diff --git a/qiskit/primitives/base/base_primitive.py b/qiskit/primitives/base/base_primitive.py
index 436c3dd1f5c4..076ed990f3a3 100644
--- a/qiskit/primitives/base/base_primitive.py
+++ b/qiskit/primitives/base/base_primitive.py
@@ -15,8 +15,7 @@
 from __future__ import annotations
 
 from abc import ABC
-from collections.abc import Sequence
-from typing import Any
+from typing import Any, cast, Union, Sequence
 
 import numpy as np
 
@@ -84,22 +83,27 @@ def _validate_parameter_values(
 
         # Support numpy ndarray
         if isinstance(parameter_values, np.ndarray):
+            parameter_values = cast(np.ndarray,parameter_values)
             parameter_values = parameter_values.tolist()
         elif isinstance(parameter_values, Sequence):
+            parameter_values = cast(Union[Sequence[Sequence[float]],Sequence[float]],parameter_values)
             parameter_values = tuple(
-                vector.tolist() if isinstance(vector, np.ndarray) else vector
+                cast(np.ndarray, vector).tolist() if isinstance(vector, np.ndarray) else vector
                 for vector in parameter_values
             )
 
         # Allow single value
         if _isreal(parameter_values):
+            parameter_values = cast(float,parameter_values)
             parameter_values = ((parameter_values,),)
         elif isinstance(parameter_values, Sequence) and not any(
             isinstance(vector, Sequence) for vector in parameter_values
         ):
+            parameter_values = cast(Sequence[float],parameter_values)
             parameter_values = (parameter_values,)
 
         # Validation
+        parameter_values = cast(Sequence[Sequence[float]], parameter_values)
         if (
             not isinstance(parameter_values, Sequence)
             or not all(isinstance(vector, Sequence) for vector in parameter_values)
@@ -132,7 +136,7 @@ def _isint(obj: Any) -> bool:
     return isinstance(obj, int_types) and not isinstance(obj, bool)
 
 
-def _isreal(obj: Any) -> bool:
+def _isreal(obj: Any) -> bool | np.bool_:
     """Check if object is a real number: int or float except ``±Inf`` and ``NaN``."""
     float_types = (float, np.floating)
     return _isint(obj) or isinstance(obj, float_types) and float("-Inf") < obj < float("Inf")