I left Jefferson City for good for the session early this morning, having made it home about 15 minutes ago, and for some reason, I was in the mood for classic country. So I hit the car radio on 730 when I got close enough to Warrenton.
Their morning DJ likes to play a station contest game called high-low. He thinks of a number between one and 100, and takes rapid succession calls from people who guess the number. I would presume that it’s an iterative process, that he’ll say the caller’s guess is too high or too low, and eventually someone will get the right answer iteratively.
However, when he played the game this morning, someone got the right number on the very first call.
“What were the odds?,” I thought. Must be somewhere in the blue moon to Powerball range.
Since it’s between one and 100, there’s a 1% chance that someone will nail it on the very first call with every given game. That’s 2.9 million times better odds than Powerball.
Now, let’s work backwards to see the odds of this happening over time.
Since there’s a 1% chance that it does happen, it means there’s a 99% chance that it doesn’t happen. You have to raise 0.99 to the power of x, x being the number of games played, to find the odds that it doesn’t happen in all x games, then subtract that from 1 to see the odds that it does happen at least once in x games. So, in 10 games, there’s a 9.6% chance that will happen, in 50 games, 39.5%, and in 100 games, 63.4%. If he plays one game per weekday, which would be 260 per year, let’s say 250 because of holidays, it means that there’s a 91.9% in every given year that at least once, someone will nail it on the first call.
Alternatively, do (log 0.5)/(log 0.99) to figure how many games it would take for the odds of it happening to be 0.5, or 50%. The answer is almost 69, which means the odds of it happening are even money once every 14 weeks, again, assuming one game per weekday.
So, it’s not that rare.