I was using an online app called "GeoGuessr" where you guess the location on a world map of a given Google Street view image. On one certain attempt, I picked a location within 92.7 square miles of the actual location.
I am intrigued by figuring out the statistical probability of guessing a random point that's within a given number of units squared. In this case, I am trying to find the probability of picking a point this close using random guessing.
The earth's total surface area, A is 196.9 million square miles. I found a point q within 92.7 square miles of p.
I figure the probability of guessing that a random point is within 1 square mile of the actual location is 1:196900000. For a range up to 92.7, I divide 196,900,000 by 92.7 yielding ~ 1:2124056.
Is my arithmetic correct? If not, how should I solve the problem?