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## Main Question or Discussion Point

Given that there are N events, and the probability of each event is equal to the other and each probability is equal to 1 (ex. P(B1)=P(B2)=P(B3)...=P(BN)=1, we can show by induction that P(B1B2B3...BN)=1. If the collection of these N events are countably infinite or uncountably infinite, how would each affect the fact that P(B1B2...BN)=1?

My initial thoughts are that countably infinite collections can add up to 1, but with uncountably infinite the probabilities will be 0. But in this instance, we are given that P(B1)=P(B2)...=P(BN)=1. Does it make a difference if the set is countably infinite? How about if it is uncountably infinite?

My initial thoughts are that countably infinite collections can add up to 1, but with uncountably infinite the probabilities will be 0. But in this instance, we are given that P(B1)=P(B2)...=P(BN)=1. Does it make a difference if the set is countably infinite? How about if it is uncountably infinite?