diff --git a/numpy/random/mtrand/mtrand.pyx b/numpy/random/mtrand/mtrand.pyx
index b45b3146f145..6aba88f18fc4 100644
--- a/numpy/random/mtrand/mtrand.pyx
+++ b/numpy/random/mtrand/mtrand.pyx
@@ -1142,7 +1142,9 @@ cdef class RandomState:
                 raise ValueError("a and p must have same size")
             if np.logical_or.reduce(p < 0):
                 raise ValueError("probabilities are not non-negative")
-            if abs(kahan_sum(pix, d) - 1.) > atol:
+
+            # negated to handle NaNs in p
+            if not abs(kahan_sum(pix, d) - 1.) <= atol:
                 raise ValueError("probabilities do not sum to 1")
 
         shape = size
diff --git a/numpy/random/tests/test_random.py b/numpy/random/tests/test_random.py
index 61c6e912dae6..53d0d67ae3f1 100644
--- a/numpy/random/tests/test_random.py
+++ b/numpy/random/tests/test_random.py
@@ -403,6 +403,8 @@ def test_choice_exceptions(self):
         assert_raises(ValueError, sample, [1, 2, 3], 4, replace=False)
         assert_raises(ValueError, sample, [1, 2, 3], 2,
                       replace=False, p=[1, 0, 0])
+        with np.errstate(invalid='ignore'):
+            assert_raises(ValueError, sample, [42, 2, 3], p=[None, None, None])
 
     def test_choice_return_shape(self):
         p = [0.1, 0.9]