In this work, we analyze the privacy guarantees of Zigbee protocol, an energy-efficient wireless IoT protocol that is increasingly being deployed in smart home settings. Specifically, we devise two passive inference techniques to demonstrate how a passive eavesdropper, located outside the smart home, can reliably identify in-home devices or events from the encrypted wireless Zigbee traffic by 1) inferring a single application layer (APL) command in the event's traffic burst, and 2) exploiting the device's periodic reporting pattern and interval. This enables an attacker to infer user's habits or determine if the smart home is vulnerable to unauthorized entry. We evaluated our techniques on 19 unique Zigbee devices across several categories and 5 popular smart hubs in three different scenarios: i) controlled shield, ii) living smart-home IoT lab, and iii) third-party Zigbee captures. Our results indicate over 85% accuracy in determining events and devices using the command inference approach, without the need of a-priori device signatures, and 99.8% accuracy in determining known devices using the periodic reporting approach. In addition, we identified APL commands in a third party capture file with 90.6% accuracy. Through this work, we highlight the trade-off between designing a low-power, low-cost wireless network and achieving privacy guarantees.