Really annoyed me that the kiddos voted to not switch, and they got the car. Getting children to understand that 1/3 is smaller than 1/2 is hard enough. I’m going to program my own evil version that only wins on switch the first time next time I do this.
Change the problem from 3 doors to a million. Kids pick a door, and the host opens 999,998 doors, leaving theirs and one other door closed. One of the closed doors is the winner. Do they want to switch now?
This is a good way to think about it, because the three door version makes it almost seem like the host is guessing. But if you pick door #8 and the host eliminates every door except #8 and, for some reason, #682,025, are you more confident in 8 or 682,025?
That’s a good idea. I went with redoing the sim a few times and then also doing stuff with a plinko game, which seemed to help them get it.
The first couple plinko runs also were really annoying for bellcurve purposes tho.
I explained this to my programmer colleagues. My explanation was lacking so they wrote a numerical simulation and ran it a few million times to be sure.
They were convinced.
It’s called Monte Carlo method, I presume.
I talked a little about Monte Carlo methods too - told them about a FORTRAN (!) program I had to write in college. Finding pi by throwing darts at a dart board and looking at the ratio of hits to misses to determine area…
LOL I did this too when I first heard the solution.
I was like “no, that cant be right”. Then ran the test and was surprised by the result.
Have you played the Cliff Hangers music to those children, because if so I love you.
https://youtu.be/HjT7bSHAHAU
Oh this makes it so much more intuitive. I’m gonna use that in the future