diff --git a/tests/test_synth.py b/tests/test_synth.py
index 5f4a2ca..ede8b77 100644
--- a/tests/test_synth.py
+++ b/tests/test_synth.py
@@ -1,4 +1,36 @@
 from pm_bench import _synth
+from pm_bench._synth import is_positive_outcome
+
+
+def test_is_positive_outcome_true_when_ends_with_delivery_confirmed() -> None:
+    assert is_positive_outcome(["received", "ship_order", "delivery_confirmed"])
+
+
+def test_is_positive_outcome_false_when_ends_with_other_activity() -> None:
+    assert not is_positive_outcome(["received", "ship_order"])
+
+
+def test_is_positive_outcome_false_on_empty_list() -> None:
+    assert not is_positive_outcome([])
+
+
+def test_is_positive_outcome_false_when_delivery_confirmed_not_last() -> None:
+    assert not is_positive_outcome(["delivery_confirmed", "received"])
+
+
+def test_is_positive_outcome_true_on_single_event_delivery_confirmed() -> None:
+    assert is_positive_outcome(["delivery_confirmed"])
+
+
+def test_synthetic_log_positive_rate_matches_paths_weight() -> None:
+    """PATHS[4] has weight 0.10; rate on a large sample should be close."""
+    events = list(_synth.synthetic_log(n_cases=500, seed=42))
+    by_case: dict[str, list[str]] = {}
+    for cid, act, _ in events:
+        by_case.setdefault(cid, []).append(act)
+    positives = sum(1 for acts in by_case.values() if is_positive_outcome(acts))
+    rate = positives / len(by_case)
+    assert 0.05 <= rate <= 0.20, f"positive rate {rate:.3f} outside expected range"
 
 
 def test_deterministic() -> None: