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Banach's matchbox problem

problem in probability: Banach has 2 matchboxes (initially with 𝑁 matches) in left and right pockets; if he reaches into his pocket and finds for the 1st time that the box picked is empty, what’s the probability that there are 𝑘 matches in the other?

Pronunciation
/ˈbænəks ˈmæʧˌbɑks ˈprɑbləm/
/Banach's ˈmaʧbɒks ˈprɒbləm/