MathDB

Let

f(x, y) = \left\lfloor \frac{5x}{2y} \right\rfloor + \left\lceil \frac{5y}{2x} \right\rceil

. Suppose

x, y

are chosen independently uniformly at random from the interval

(0, 1]

. Let

p

be the probability that

f(x, y) < 6

. If

p

can be expressed in the form

m/n

for relatively prime positive integers

m

and

n

, compute

m + n

.
(Note:

\lfloor x\rfloor

is defined as the greatest integer less than or equal to

x

and

\lceil x \rceil

is defined as the least integer greater than or equal to

x

Problem Statement