diff --git a/stdlib/3/random.pyi b/stdlib/3/random.pyi
index ee3cbda65..439f9b520 100644
--- a/stdlib/3/random.pyi
+++ b/stdlib/3/random.pyi
@@ -18,7 +18,7 @@ class Random(_random.Random):
     def getstate(self) -> Tuple[Any, ...]: ...
     def setstate(self, state: Tuple[Any, ...]) -> None: ...
     def getrandbits(self, __k: int) -> int: ...
-    def randrange(self, start: int, stop: Union[int, None] = ..., step: int = ...) -> int: ...
+    def randrange(self, start: int, stop: Optional[int] = ..., step: int = ...) -> int: ...
     def randint(self, a: int, b: int) -> int: ...
     if sys.version_info >= (3, 9):
         def randbytes(self, n: int) -> bytes: ...
@@ -32,7 +32,7 @@ class Random(_random.Random):
             cum_weights: Optional[Sequence[float]] = ...,
             k: int = ...,
         ) -> List[_T]: ...
-    def shuffle(self, x: MutableSequence[Any], random: Union[Callable[[], float], None] = ...) -> None: ...
+    def shuffle(self, x: MutableSequence[Any], random: Optional[Callable[[], float]] = ...) -> None: ...
     if sys.version_info >= (3, 9):
         def sample(
             self, population: Union[Sequence[_T], AbstractSet[_T]], k: int, *, counts: Optional[Iterable[_T]] = ...
@@ -77,7 +77,7 @@ if sys.version_info >= (3, 6):
         k: int = ...,
     ) -> List[_T]: ...
 
-def shuffle(x: MutableSequence[Any], random: Union[Callable[[], float], None] = ...) -> None: ...
+def shuffle(x: MutableSequence[Any], random: Optional[Callable[[], float]] = ...) -> None: ...
 
 if sys.version_info >= (3, 9):
     def sample(population: Union[Sequence[_T], AbstractSet[_T]], k: int, *, counts: Optional[Iterable[_T]] = ...) -> List[_T]: ...