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Find out why the formula we use to work out conditional probabilities is true!
Think about it. At the start with the 1-1+1-1+.... Being wrong, is simply wrong. Because of the part where they say 1-1+1-1+1-....+1-1+1-1+1-1+.... is as wrong as putting decimals after a repeating number. Even if this is true, you are assuming that the sum ends with -1. in order to have the second sum start with +1 which is absurd because if the sum ends with -1 (which defeats the purpose anyway) then Z=0. And if Z=0 then 2Z=Z is true. Because 0+0=0 not to mention that it isn't even the original sum anymore.