diff --git a/Doc/library/random.rst b/Doc/library/random.rst
index 78c3cc0bedc..b6b0b6c4daf 100644
--- a/Doc/library/random.rst
+++ b/Doc/library/random.rst
@@ -191,6 +191,8 @@ be found in any statistics text.
    Return a random floating point number *N* such that ``a <= N <= b`` for
    ``a <= b`` and ``b <= N <= a`` for ``b < a``.
 
+   The end-point value ``b`` may or may not be included in the range
+   depending on floating-point rounding in the equation ``a + (b-a) * random()``.
 
 .. function:: triangular(low, high, mode)
 
diff --git a/Lib/random.py b/Lib/random.py
index 8b4c38edb17..568de88e636 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -349,7 +349,7 @@ class Random(_random.Random):
 ## -------------------- uniform distribution -------------------
 
     def uniform(self, a, b):
-        """Get a random number in the range [a, b)."""
+        "Get a random number in the range [a, b) or [a, b] depending on rounding."
         return a + (b-a) * self.random()
 
 ## -------------------- triangular --------------------