Friday Maths Problem Options

[MonkeyFiend]

I'm bored, so I thought I'd annoy you with a mathematical puzzle...a nice simple one though.....

Monkeyfiend has 3 boxes: 1,2 & 3.

In one of the boxes is £1000000, the others contain something rubbish. You pick a box, say box No.1 and MonkeyFiend (who knows whats in each of the boxes), opens another box, say box 3, which contains a rubbish prize. Monkeyfiend then says do you want to pick box No.2 or stay with your original choice of box 1?

Which should you do and why?

[Jearik]

The answer to the math problem

I did horrible probability in College

If one of 3 boxes contains fun, that means that each box has 33.33% chance of having fun

so to summarise
Box 1 = 33.33%
Box 2 = 33.33%
Box 3 = 33.33%

But wait.. monkey opens Box 3 and laughs in your face saying what now?

Box 1 still has 33.33% chance of having fun however
Box 2 is now 66.66% chance of having goodies inside why? here's the tricky semantics

Box 1 has a 33.33% chance of having goodies, which means that there is a 66.66% chance of goodies NOT being in there..
So when Box 2 and 3 where there, the probability of fun NOT being in box 1 was 66.66% split two ways into box 2 and 3...
but since box 3 is taken away then that 66.66% chance of NOT being in box 1 and being in box 2 and 3, can now be interrupted as a 66.66% chance of fun being in box 2 alone.

I hope you followed