Heads or Tails

2/3

I believe it's one out of two.
Markr: I believe that you have this confused with the common door problem where you pick a door, a door is shown to have the unfavorable outcome and then you're asked whether or not you want to switch doors. In that case, your answer would be right. However, In this case, there are two quarters. Either way you pick, the initial value is heads. When you flip it over, there are only two possibilities, heads and tails, and I'm not seeing any reason why one outcome would be more likely than the other, so it should be heads 1/2 times.

Actually, Mark is right. There are three possibilities involving pulling a heads first, and two out of those three involve a head on the opposite side.

I'm not going to challenge markr where math is concerned but I don't see the answer, if you are looking at a "head" and the only possibility is that the other side is head or tail, how can it not be 50/50

Say the coins are H1/T and H2/H3 (one side/other side).

When you pick a coin and see a head, it is one of these cases (what you see/other side):
H1/T
H2/H3
H3/H2

I'm gonna go test this. It's still not seeming right to me. All we know is that there are two coins, call them C1 and C2. C1 has two heads, and C2 has a head and a tail. You draw a coin, not knowing if it's C1 or C2, and see a head. I see two cases. The drawn coin is C1 or it's C2. If it's C1, you see a head on the other side. If it's C2, you'll see tails. Since both coins are equally as likely to be drawn, it still seems to be 1 out of 2 to me.

But both coins are not equally likely to be drawn and present 'heads.'

That's correct.

H1/T occurs with probability .25
H2/H3 occurs with probability .25
H3/H2 occurs with probability .25
T/H1 doesn't occur (per the problem statement)

so here i am replying a month late and wrong too...
it clicked