Uh oh, here we go: CBS claims Pats win coin flip at "impossible clip"

[raduray]

The probability of hitting the specific point, or any specific point for that matter, is 0. You can think of the probability as an area. In this case, the area of any specific point is 0 (it has no height or width.)

That assumes the tip of the dart is also a point, which is not true. The dart can hit in the vicinity of the target point and the tip's cross section area will span the target point. An engineer's perspective

 

[FourierSeries]

If you consider the tip of the dart a point, then your odds are 0. You can't hit a point with another point.

However, when I throw a dart into a dartboard, it leaves a roughly 1 mm in diameter hole in the board. If you select a point on the board, then it is possible I hit that point because it is possible that the point lies within the 1 mm range I've created.

For example, suppose a computer selected a random number between 1 and 2. Because there are an infinite amount of numbers between 1 and 2, the odds of me guessing it correctly are zero, no matter how many guesses you gave me. But since the range between 1 and 2 is finite, then if I gave a range such as "the number is between 1.1 and 1.2" there would be a 10% chance I was correct.

Well, by point I meant point as defined in Euclidean geometry (perhaps I should have explicitly stated that.) So yes, the example requires an ideal dart which has a point for a tip, but I think you'll find that even a real dart very closely satisfies this property. Nevertheless, in a practical scenario, the probability is still near zero.

The example is an idealization, but then again, probability theory is also an idealization of the real world. "Probability of 0" doesn't mean impossible, as explained earlier using the concept of "almost surely/almost never" borrowed from measure theory.