We investigate the variations in the probabilities of complex sunspot groups (SGs)-large, asymmetric, or delta-type SGs-producing X-ray flares (>= M1) in solar cycles (SCs) 22, 23, and 24 based on the SG data collected by the United States Air Force/Mount Wilson Observatory and the flare data recorded by Geostationary Operational Environmental Satellites. The following are the main findings. (1) For complex SGs in the whole disk as well as the northern and southern hemispheres during SC 22, their numbers and probabilities of producing flares change almost synchronously. (2) For complex SGs during SC 23, probabilities of producing flares during the early declining phase in the whole disk do not decrease with decreasing complex SG number; in the northern hemisphere, the probability of producing flares during the declining phase is significantly higher than that during the maximum phase; in the southern hemisphere, there is no definite variation trend in the probabilities of producing flares during the maximum and declining phases. (3) For complex SGs during SC 24, the probabilities of producing flares during the later rising and early declining phases are significantly higher than or comparable to those during the maximum phase no matter how their numbers change; in the northern hemisphere, the probability of producing flares during the rising phase is significantly higher than or at least comparable to that during the maximum phase; in the southern hemisphere, there is no definite variation trend in the probabilities of producing flares during the maximum and declining phases.