Two Random Numbers, One Hyperbola, and 15.3 Percent
Draw X and Y uniformly from the unit interval and their product beats a half with probability (1 - ln 2)/2, about 15.3 percent. The reflex answer of a quarter counts a condition that is genuinely necessary and treats it as sufficient, which is why 0.8 times 0.6 sits inside the quarter square and still loses. The hyperbola y = 1/(2x) cuts the winners down to a sliver, and one integral measures it.