Question of the week · Maths Methods
You pick a box. I open an empty one. Stay or switch?
Predict
A prize is in one of three boxes. You pick box 1. The host, who knows where it is, opens an empty box. Should you switch?
Test it
Play a few rounds, then let it run 100 games each way.
Why
Answer: Switch
Your first pick is right 1 time in 3, so 2 times in 3 the prize is in one of the other boxes.
The host knows where the prize is and always opens an empty box, so opening it tells you nothing new about box 1. The whole 2/3 now sits on the box you can switch to: switching doubles your chances.
You know it. Now explain it.
The exam asks you to write this out. Write your explanation and get it marked point by point, with exactly what to add for the marks you miss.
Get my answer markedFree to start · No card needed · AI marks are practice estimates.