The activities of geomagnetic storms are generally controlled by solar activities. The current solar cycle (SC) 24 is found to be mild; compared to SCs 19–23, the storm occurrence and size derived by averaging the occurrence number and Dst around the solar maximum are reduced by about 50–82% and 36–61%, respectively. We estimate separately, for SC 19 to 24, the repeat intervals between geomagnetic storms of specific Dst, based on fits of power-law and log-normal distributions to the storm data for each SC. Repeat intervals between super geomagnetic storms with Dst≤–250 nT are found to be 0.36–2.95 year(s) for SCs 19–23, but about 20 years based on the data for SC 24. We also estimate the repeat intervals between coronal mass ejections (CMEs) of specific speed (VCME) since CMEs are known to be the main drivers of intense storms and the related statistics may provide information about the potential occurrence of super geomagnetic storms from the location of the Sun. Our analysis finds that a CME with VCME≥1860 km/s may occur once per 3 and 5 months in SC 23 and 24, respectively. Based on a VCME-Dst relationship, such a fast CME may cause a storm with Dst=–250 nT if arriving at the Earth. By comparing the observed geomagnetic storms to storms expected to be caused by CMEs, we derive the probability of CME caused storms, which is dependent on VCME. For a CME faster than 1860 km/s, the probability of a CME caused storm with Dst≤–250 nT is about 1/5 for SC 23 or 1/25 for SC 24. All of the above results suggest that the likelihood of the occurrence of super geomagnetic storms is significantly reduced in a mild SC.