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Coins in a box

Imagine that you have two quarters in a box and that one of the quarters had heads on both sides, while the other had heads on one side and tails on the other. Question: if you remove one of these quarters from the box and the visible side shows heads, what is the probabillity that the other side will also be heads?

John
Thursday, February 24, 2005

2/3. similar problem as before, or not?

so if you get heads there are three possibilities: you got any side of the coin with heads on both sides or the side with heads of the other coin, in the first two possibilities there's also heads on the other side -> 2/3.

tobi
Thursday, February 24, 2005

I think this is what tobi said, but let me work through it a different way:

There are two sets of coin "states" in the box:

H / H
H / T

And you randomly choose one coin, so there are 4 choices.
( ) indicates the coin you choose:

(H) / H
H / (H)
(H) / T
H / (T)

Option 4 is not valid, because you can see a head. That reduces the valid states to 3, and the chance the other side is a head is therefore 2/3.

BradC
Thursday, February 24, 2005

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