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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