In semiarid regions, periods of one to several consecutive months of scarcity of precipitation or low flow rates in rivers and streams frequently occur. In these regions, scarce precipitation considerably affects grazing activities on rangelands, irrigation agriculture, and flora and fauna of surface stream environments. This paper is concerned with estimating probabilities of occurrence for such events and associated risks by using statistical information provided by monthly precipitation and streamflow series. Conventional return period and risk concepts as customarily used in hydrology are applied, and events of interest such as meteorological droughts are considered by using monthly precipitation as a time-related series of supply, thereafter addressing hydrological droughts in terms of streamflow supply. For these two kinds of events, periodic situations of time-independent phenomena are considered for the case of precipitation, with time-dependent phenomena considered for streamflows. The method is applied to the semiarid portion of Chile to calculate probabilities of occurrence of specific numbers of consecutive months with no significant precipitation, or flow rates insufficient to meet stream ecological needs.