The probability of picking a single number can't be used to determine the probability of picking a set. You can't build intuition this way. This is almost exac

The probability of picking a single number can't be used to determine the probability of picking a set. You can't build intuition this way. This is almost exactly the same thing as saying integrating x^3 from minus infinity to plus infinity is zero because each zero width line has zero area, so adding them all up is zero too. Gives the right answer by coincidence, but also works to show incorrect results.