Fine Print: I created this page because someone posed a puzzle asking that I calculate the answer logically. This web site lets a person try to find the answer randomly. If you keep pressing SUBMIT repeatedly, it is just as random as if you randomly change your box and name selection each time. Have fun with this (not-very-well-designed) page.
I later discovered the person had asked me to solve Bertrand's Box Paradox, but with president names instead of gold and silver coins.
The names of six presidents (Obama, Clinton, Carter, Reagan, Trump, Nixon) have been hidden randomly in three identical boxes, two names per box.
- You know that
- One box holds two Democrat names.
- One box holds 2 Republican names.
- The other box holds one of each.
| - Your Goal is:
- Pick a box at random. Pick one name at random from that box.
- Given: You pulled out a Democrat's name first ...
- What is the probability that the other name in that box is also a Democrat?
|
the host revealed that the boxes contained:Box 1
Carter (D) / Clinton (D)
| Box 2
Trump (R) / Nixon (R)
| Box 3
Obama (D) / Reagan (R)
|
Note these clarifications, that I thought were obvious from the description above:
- There are only six names, three D and three R, in the three boxes.
- That makes two names per box, placed there randomly for each trial.
- There are no duplicate names.
- There could have been three boxes, each with 1R and 1D, but that possibility is eliminated by the puzzle definition.
- By definition, the three boxes include one 2D box, one 2R box, and one 1D1R (or 1R1D) box, in random order, with names in random order in that box.
- There is no possible randomization that would result in NO box with one of each.
- The person has no choice, he will pick the second name from the same box, as implied by the question above about the probability of the OTHER name from the SAME box.
- Each time you click the SUBMIT button, all names and boxes are rerandomized. Knowledge of previous trials will not affect future probability.
* Send improvement suggestions to John at domain mazes,com
Do you know PHP? I need help coding a simple Input/Output on Server to keep track of grand total of everyone's trials.
1. Delay if file tags say another client is updating file
2. But continue anyway if delay is too long
3. Tag file so other clients know file is being updated
4. Open file, read four numbers as regular Comma delimited text
5. Increment some of those values
6. Write updated numbers back to beginning of file
7. Close file
8. Untag file so next client knows file is available
* * If you have free advice, I'd love to add it to this program.