Try small values

Probability 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.

1/2 1/2 if n even, n/(2n+1) if n is odd 1/n (n-1)/n None of the above 1/2 if n is 2 or 3 mod 4, n/(2n+1) if n is 0 or 1 mod 4

1 solution

Wen Z
Jul 21, 2016

A really nice thing to notice is that the order doesn't matter... (they are independent events)

So what happens if you throw the spinner with the 1 and 2 last?

Try small values

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