Throw or die!
A -sided die is thrown times. The probability that faces, with even numbers, show up odd number of times, can be expressed as where & are coprime positive integers. What is the value of ?
The answer is 3.
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1 solution
Since you’re rolling the die an odd number of times, the amount of even and odd faces you get will either be even and odd or odd and even respectively. Because the number of faces on the die is even, there is an equal amount of even and odd faces. Due to the symmetry, any pair (a,b) denoting the amount of even and odd faces is just as likely as its inverse (b,a), so the probability of getting an even number of odd faces is the same as an odd number of odd faces. Therefor the probability is 1/2.