What is the ruling on associating the term "lottery" (al-qur'ah) with the legal division of inheritance (al-qismah al-shar'iyyah lil-irth), and what is the wisdom behind the verses of inheritance if it is possible to reach a mutual agreement or a partition (muhāyāh) in distributing the inheritance?

The division (qismah) is a jurisprudential term meaning the distinction of each partner's share from the other. It has several types according to jurists, such as division by mutual agreement (muradaha), division by alternating use (muhay’ah), and division by lot (qur'ah). Thus, the lot is a type of division, and it is a means of distinguishing a shared right. It becomes obligatory if some partners refuse division by mutual agreement or by alternating use. As for the wisdom behind the Holy Qur'an's clarification of each heir's share, it is not hidden.