diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/inference/BinomialTest.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/inference/BinomialTest.java
index 80650c9b4..a7deb3187 100644
--- a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/inference/BinomialTest.java
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/stat/inference/BinomialTest.java
@@ -138,7 +138,7 @@ public class BinomialTest {
                     if (criticalValueLow == criticalValueHigh) {
                         pTotal += pLow;
                     } else {
-                        pTotal += 2 * pLow;
+                        pTotal += 2 * Math.nextDown(pLow);
                     }
                     criticalValueLow++;
                     criticalValueHigh--;
diff --git a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/inference/BinomialTestTest.java b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/inference/BinomialTestTest.java
index bf83dfa17..f480e0b66 100644
--- a/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/inference/BinomialTestTest.java
+++ b/commons-math-legacy/src/test/java/org/apache/commons/math4/legacy/stat/inference/BinomialTestTest.java
@@ -126,4 +126,11 @@ public class BinomialTestTest {
         Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.GREATER_THAN, alpha01));
         Assert.assertFalse(testStatistic.binomialTest(trials, successes, probability, AlternativeHypothesis.LESS_THAN, alpha05));
     }
+
+    @Test
+    public void testMath1644() {
+        final BinomialTest bt = new BinomialTest();
+        final double pval = bt.binomialTest(10, 5, 0.5, AlternativeHypothesis.TWO_SIDED);
+        Assert.assertTrue("pval=" + pval, pval <= 1);
+    }
 }