We present the sympathetic eruption of a standard and a blowout coronal jet originating from two adjacent coronal bright points (CBP1 and CBP2) in a polar coronal hole, using soft X-ray and extreme-ultraviolet observations respectively taken by the Hinode and the Solar Dynamics Observatory. In the event, a collimated jet with obvious westward lateral motion first launched from CBP1, during which a small bright point appeared around CBP1's east end, and magnetic flux cancellation was observed within the eruption source region. Based on these characteristics, we interpret the observed jet as a standard jet associated with photospheric magnetic flux cancellation. About 15 minutes later, the westward-moving jet spire interacted with CBP2 and resulted in magnetic reconnection between them, which caused the formation of the second jet above CBP2 and the appearance of a bright loop system in between the two CBPs. In addition, we observed the writhing, kinking, and violent eruption of a small kink structure close to CBP2's west end but inside the jet base, which made the second jet brighter and broader than the first one. These features suggest that the second jet should be a blowout jet triggered by the magnetic reconnection between CBP2 and the spire of the first jet. We conclude that the two successive jets were physically connected to each other rather than a temporal coincidence, and this observation also suggests that coronal jets can be triggered by external eruptions or disturbances, as well as internal magnetic activities or magnetohydrodynamic instabilities.