Try small values

Discrete Mathematics Level pending

Suppose I have $$n>1$$ spinners, each labelled a different integer between $$1$$ and $$n$$ inclusive, such that the ith spinner has the numbers $$1,2,\ldots,i$$ with a $$\dfrac{1}{i}$$ chance of each occurring. Suppose I toss all the spinners at once.

What is the probability that the sum is an even number?

Hint: this is a trick question.

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