Patient doses cannot be limited; instead, radiological examinations should be justified and optimized to ensure the necessary diagnostic or therapeutic effect with the lowest patient dose achievable. Assessment of the radiation risks from patient exposure is important part of the justification process. Hence, medical staff within the framework of their professional activities should possess necessary information on the data on radiation risk from different types of radiological procedures. An approach has been developed that allows considering age and gender dependences of the risk coefficients of radiogenic cancer and the age and gender distribution of patients for various radiological examinations to assess the individual radiation risk for patient and collective risk for population from medical exposure. The approach is based on a new expanded use of the effective dose concept proposed in ICRP Publication 147 and demonstrated using the medical exposure in the Russian Federation as the example. For 30 radiological examinations that compose about 80% of the collective dose from medical exposure of the public in the Russian Federation radiation risk was assessed based on calculated age and gender specific risk coefficients per unit effective dose. For the rest of the examinations a simplified approach was used to assess the risk, which was based on using an age and gender specific risk coefficient determined for one of 4 anatomical regions (head, neck, chest and abdomen) or for uniform irradiation of the whole body. The proposed approach allows significantly improving the assessment of the radiation risk while continuing to use the effective dose as a dosimetric quantity within the framework of the state program in the Russian Federation. As a result the collective risk from medical examinations in the Russian Federation in 2022 was lower by the factor of 3 compared to the previous assessment based on the effective dose with the nominal risk coefficient.