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Each ball can be even (e) or odd (o).
If there are two balls they could be ee, eo or oo. These are three possibilities. There needs to be an even number of possibilities for there to be a chance that the probability of the total being 1 in 2 as a half.
If there are three balls they could be eee, eeo, eoo or ooo. There are four possibilities. The totals are e, o, e and o. The probability therefore equals a half which is what we want.
If there are four balls they could be eeee, eeeo, eeoo or oooo. There are an odd number of possibilities so you cannot have a probability of a half.
So there must be an odd number of balls to have an even number of possibilities.