Dear Elly (I hope it's okay that I have a pet name for you in my head),
That djinni sounds like a meanie. Hopefully this information will help you out with your strange predicament.
According to this website, Earth's total land area is about 1.5x108 km2. According to Google, Antarctica's land area is 1.4x107 km2. So that means there is 1.36x108 km2 of land that you could get teleported to.
Also according to Google, the land area of the United States is about 9.8x106 km2.
And a circle with a 5 km (about 3 miles, which I would consider walking distance) radius around a hypothetical point at the middle of BYU would have an area of 78.5 km2.
So the probability of randomly teleporting into the US would be 7.206% (9.8x106 km2/1.36x108 km2). And the probability of randomly teleporting to BYU would be 0.00577% (78.5 km2/1.36x108 km2).
Okay. So now we can do math.
Just a quick disclaimer: I'm not a mathematician and I will be the first to admit that my solutions are not the most elegant. I hope that this won't be too difficult to follow.
If the likelihood of teleporting into the US is 7.206% (0.07206), that means that there is a 92.79% (0.9279) chance of teleporting not into the US.
So if were to multiply 0.9279 and 0.9279 to get 0.8611, that would mean that the probability of not teleporting to the US after two teleports was 86.11%.
All we need to do now is figure out how many times we need to multiply 0.9279 by itself in order to get 50%, which would represent the number of times on average it would take you to teleport into the US. In other words, this can be solved with a logarithm!
In this equation, y=the number of teleports and x=the probability of not teleporting to the US after y number of times. Similarly, the equation for teleporting to within a 5 km radius of BYU would look like this:
When we solve the equation for the US,
We find that the average number of teleports needed for teleportation to the US is 9.3.
When we solve the equation for within walking distance from BYU,
We find that the average number of teleports needed for teleportation to within walking distance of BYU is 12012.
Best of luck with this big life change, my friend.