diff --git a/pymc_marketing/clv/distributions.py b/pymc_marketing/clv/distributions.py
index 3160282d..49864ae9 100644
--- a/pymc_marketing/clv/distributions.py
+++ b/pymc_marketing/clv/distributions.py
@@ -783,7 +783,9 @@ def sim_data(lam, p, T):
             t = 0  # recency
             n = 0  # frequency
 
-            churn = p  # MBG/NBD customer active with probability p at time 0
+            churn = (
+                rng.random() < p
+            )  # MBG/NBD customer active with probability p at time 0
             wait = rng.exponential(scale=1 / lam)
 
             while t + wait < T and not churn: