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Non-technical summary: This study provides methods and examples to calculate the probability of inundation from tsunamis in coastal areas. Following the framework used for earthquake probability, we show that, with some additional features unique to tsunamis, long-term forecasts can be useful tools for preparedness. In some regions like Acapulco, Mexico, there is a long record of tsunami occurrence sufficient to calculate the likelihood of future events. In other places, like the U.S. Pacific Northwest, the observed record is too short. We demonstrate methods for modeling a range of possible earthquake sources that generate scenario tsunamis. In addition, coastal zones may be vulnerable to tsunamis that originate far away. We thus show methods to account for the background odds of far-field tsunamis striking the coastline