The probability to observe a specific number of strange and multi-strange hadrons (nS), denoted as P(nS), is measured by ALICE at midrapidity (|y| < 0.5) in $$\sqrt{s}=5.02$$ TeV proton-proton (pp) collisions, dividing events into several multiplicity-density classes. Exploiting, for the first time, a technique based on counting the number of strange-particle candidates event-by-event, this measurement allows one to extend the study of strangeness production beyond the mean of the distribution. This constitutes a new test bench for production mechanisms, probing events with a large imbalance between strange and non-strange content. The analysis of a large-statistics data sample makes it possible to extract P(nS) up to a maximum nS of 7 for $${\text{K}}_{\text{S}}^{0}$$, 5 for Λ and $$\overline{\Lambda }$$, 4 for Ξ− and $${\overline{\Xi } }^{+}$$, and 2 for Ω− and $${\overline{\Omega } }^{+}$$. From this, the probability of producing strange hadron multiplets per event is calculated,...
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