Rocket golf, hole in one

According to what-if.xkcd/85 if you had a bag of golf balls that was 150 miles in diameter you would be statistically likely to hit-a-hole in one at every golf course in the world. I was just curious as to what, "statistically likely" means. I remember from my statistics class back in my college days that statistically significant means greater than 1%, which isn't very significant.

So first things first, how many golf courses are in the world? Google says there are 32,000 ish golf courses in the world over half of which are in the US (17,000). In Randall's scenario you evenly spread your golf balls across the middle latitudes, the US is not in the middle lattitudes which means it is statistically impossible to score a hole in over half the courses in the world. We're going to have evenly spread our balls out across everything but the arctic and antarctic circles.

Wikipedia says that each golf course is roughly 125 acres and has 18 holes (some have 9, most have 18, and others have 27 or even 36). 125 acres is roughly .2 miles². The about golf website says all golf holes are 4.25 in. in diameter or 2.125 in. in radius, or 14.2 in². That gives us a total size of 255.6 in² per golf course of hole in which to land a single golf ball. If I were to randomly drop a single golf ball onto a 125 acre golf course about 1 in 3.14 million times it would land in a hole. Minus the arctic and antarctic circles the Earth has roughly 177,100,000 miles². If I were to randomly drop a golf ball on the Earth (minus the arctic and antarctic circles), about 1 in 2,780,000,000,000,000 times it would result in a hole in one.

Each golf ball has a volume of 2.48 in³ and our sphere of golf balls has a volume of roughly 4.5 x 10²⁰ in³.
However as Randall pointed out, golf balls pack inefficiently and we can only use 65% of that space for golf balls. So we have a total of 1.8 x 10²⁰ golf balls for a total of 6.65 x 10¹¹ golf balls per mile² or better put 166 golf balls per in². I definitely should've started with the number of golf balls calculations because that would've saved me a lot of time, but here we are. Since everything but the poles are covered in 23 feet of golf balls, it is statistically impossible for you to not get a hole in one at every golf course unless all the golf balls are rocketed off your space ship at the same time and form a bridge over the golf hole. I mean we could add the poles and we'd still be covered in 21 feet of golf balls.