Originally Posted by

**Nath** I still can't agree it's 1/3 at an intuitive level. For example, when I run a analogous scenario throwing coins, I get the same result of 1/2:

I define 2 sets c1 & c2, each containing the set of possible states each of the coins can take after each is thrown:

c1 = {H1, T1}

c2 = {H2, T2}

Throwing both coins at the same time gives the following set of possibilities:

{H1, H2}

{H1, T2}

{H2, T1}

{T1, T2}

So I throw the 2 coins so that you can see them when they land, but I cannot. You tell me that one of the coins is in a state that is a member of the set {T1, T2}. You then ask me the probability that the other coin is in a state that is also a member of this same set. The set {H1, H2} is therefore eliminated, leaving the following possibilities:

{H1, T2}

{H2, T1}

{T1, T2}

But if a throw of c2 gives T2, then {H2, T1} is eliminated, so there remains a 50% chance that c1 = H1 and a 50% chance that c1 = T1

Conversely, if a throw of c1 gives T1, then {H1, T2} is eliminated, so there remains a 50% chance that c2 = H2 and 50% chance that c2 = T2.