The San Andreas, San Jacinto, and Imperial faults in California are divided into 19 segments; conditional probabilities are calculated that a particular segment will be the site of a large plate rupturing earthquake, i.e., an event that breaks the entire down-dip extent of the seismogenic zone, during the next 20 years. The sizes of such events, which account for most of the slip that occurs seismically, appear to vary greatly for different segments of these faults. Repeat time of large shocks, coseismic displacement, moment release, rupture length, and seismic magnitude appear to correlated with one another and to be a function of the tectonic style of different parts of those fault zones. Tectonic inhomogeneities on a scale of about 1 to 100 km are much larger than displacement in any single seismic event and may be regarded as being invariant in their effects upon earthquake generation over many cycles of large shocks. It is this invariance that appears to lead to a given segment of a fault rupturing repeatedly in events of nearly the same size. Since repeat time varies, however, for a given segment of a fault, a simple probabilistic approach is used to forecast the likelihood of large future earthquakes for each segment, using as input the time of the last large shock, the average recurrence time, and the standard deviation of time intervals between events. Dates of the last large shocks are available for most of the segments investigated. Repeat times are estimated from times of historic and prehistoric events, tectonic similarity, and times calculated from coseismic displacement in the last large shock divided by a rate of fault motion or strain buildup. The standard deviation of time intervals divided by the average repeat time is close to 1/3 for three fault segments in California for which data are available on historic and prehistoric earthquakes, that normalized value is adopted for all calculations of conditional probability. Magnitudes and seismic moments of future plate rupturing events are estimated for each fault segment. Several of the segments have well-constrained probabilities for rupture during the next 20 years, wheres others have large uncertainties. Eight of the segments, constituting about 40% of the total lengths of the three faults, have moderate to high probability and thus should be instrumented and studied extensively so as to provide shorter time warnings. In some cases two adjacent segments may be nearly in phase in their loading history and may break in a single event. The segment of the San Andreas fault from opposite San Jose to San Juan Bautista, which ruptured less than 1.5 m in 1906 and which probably also broke in 1938, is calculated to have a moderate to high probability of an earthquake of magnitude 6 3/4 to 7 1/4 during the next 20 years. A 325 km section of the southern San Andreas between Tejon Pass and the Salton Sea has about a 25% chance of rupturing in a shock of magnitude near 8 during the next 20 years. All the other segments have only a small chance (i.e., less than 5 to 10%) of rupturing in an event of magnitude near 8 during that interval.