/sci/ - Science & Math

Problems at: http://math.harvard.edu/putnam/
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Two real numbers <span class="math">x[/spoiler] and <span class="math">y[/spoiler] are chosen at random in the interval (0,1)
with respect to the uniform distribution. What is the probability that
the closest integer to <span class="math">x/y[/spoiler] is even? Express the answer in the form
<span class="math">r+s\pi[/spoiler], where <span class="math">r[/spoiler] and <span class="math">s[/spoiler] are rational numbers.

Two real numbers <span class="math">x[/spoiler] and <span class="math">y[/spoiler] are chosen at random in the interval <span class="math">(0,1)[/spoiler] with respect to the uniform distribution. What is the probability that the closest integer to <span class="math">x/y[/spoiler] is even? Express the answer in the form <span class="math">r+s\pi[/spoiler], where <span class="math">r[/spoiler] and <span class="math">s[/spoiler] are rational numbers.