bpo-41773: Raise exception for non-finite weights in random.choices().  (GH-22441)

diff --git a/Lib/random.py b/Lib/random.py
index 3ea369b..139e8a4 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -48,7 +48,7 @@
 from warnings import warn as _warn
 from math import log as _log, exp as _exp, pi as _pi, e as _e, ceil as _ceil
 from math import sqrt as _sqrt, acos as _acos, cos as _cos, sin as _sin
-from math import tau as TWOPI, floor as _floor
+from math import tau as TWOPI, floor as _floor, isfinite as _isfinite
 from os import urandom as _urandom
 from _collections_abc import Set as _Set, Sequence as _Sequence
 from itertools import accumulate as _accumulate, repeat as _repeat
@@ -492,6 +492,8 @@
         total = cum_weights[-1] + 0.0   # convert to float
         if total <= 0.0:
             raise ValueError('Total of weights must be greater than zero')
+        if not _isfinite(total):
+            raise ValueError('Total of weights must be finite')
         bisect = _bisect
         hi = n - 1
         return [population[bisect(cum_weights, random() * total, 0, hi)]
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index a80e71e..0c1fdee 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -324,6 +324,22 @@
         with self.assertRaises(ValueError):
             self.gen.choices('AB', [0.0, 0.0])
 
+    def test_choices_negative_total(self):
+        with self.assertRaises(ValueError):
+            self.gen.choices('ABC', [3, -5, 1])
+
+    def test_choices_infinite_total(self):
+        with self.assertRaises(ValueError):
+            self.gen.choices('A', [float('inf')])
+        with self.assertRaises(ValueError):
+            self.gen.choices('AB', [0.0, float('inf')])
+        with self.assertRaises(ValueError):
+            self.gen.choices('AB', [-float('inf'), 123])
+        with self.assertRaises(ValueError):
+            self.gen.choices('AB', [0.0, float('nan')])
+        with self.assertRaises(ValueError):
+            self.gen.choices('AB', [float('-inf'), float('inf')])
+
     def test_gauss(self):
         # Ensure that the seed() method initializes all the hidden state.  In
         # particular, through 2.2.1 it failed to reset a piece of state used