Context. Our understanding of stellar systems depends on the adopted interpretation of the initial mass function, IMF φ(m). Unfortunately, there is not a common interpretation of the IMF, which leads to different methodologies and diverging analysis of observational data. Aims: We study the correlation between the most massive star that a cluster would host, mmax, and its total mass into stars, ℳ, as an example where different views of the IMF lead to different results. Methods: We assume that the IMF is a probability distribution function and analyze the mmax - ℳ correlation within this context. We also examine the meaning of the equation used to derive a theoretical ℳ - hat{m_max} relationship, N × inthat m_maxm_up φ(m) dm = 1 with N the total number of stars in the system, according to different interpretations of the IMF. Results: We find that only a probabilistic interpretation of the IMF, where stellar masses are identically independent distributed random variables, provides a self-consistent result. Neither ℳ nor the total number of stars in the cluster, N, can be used as IMF scaling factors. In addition, hat{m_max} is a characteristic maximum stellar mass in the cluster, but not the actual maximum stellar mass. A ⟨ℳ⟩ - hat{m_max} correlation is a natural result of a probabilistic interpretation of the IMF; however, the distribution of observational data in the N (or ℳ) - mmax plane includes a dependence on the distribution of the total number of stars, N (and ℳ), in the system, ΦN(N), which is not usually taken into consideration. Conclusions: We conclude that a random sampling IMF is not in contradiction to a possible mmax - ℳ physical law. However, such a law cannot be obtained from IMF algebraic manipulation or included analytically in the IMF functional form. The possible physical information that would be obtained from the N (or ℳ) - mmax correlation is closely linked with the Φℳ(ℳ) and ΦN(N) distributions; hence it depends on the star formation process and the assumed definition of stellar cluster.