Situation A: Once only, I toss 2 identical fair coins and don't look at the outcomes. A truthful observer looks at one of the coins and tells me that at least one of the coins is a head.
Situation B: Once only, I toss 2 identical fair coins and don't look at the outcomes. A truthful observer looks at both of the coins and tells me that at least one of the coins is a head.
In A, what is the probability that there are 2 heads?
In B, what is the probability that there are 2 heads?
Aren't both probabilities 1/2?
EDIT
Let me refine the question. The agreement I have with the observer is this:
1) I will toss 2 identical coins.
2) In situation A a third party will cover the coins with a cloth. The observer will look only at the outcome of the coin that comes to rest nearest him and report it to me. What is the probability that the second outcome will be the same as the first?
3) In situation B the observer will look at both outcomes and report only the state (heads or tails) of the coin that came to rest nearest him. What is the probability that the second outcome will be the same as the first?
2nd EDIT
Changing 3) above to: 3) In situation B the observer will look at both outcomes, choose one of them, and truthfully report, "There is at least one heads", or "There is at least one tails", whichever is the case. What is the probability that the second outcome (that of the other coin) will be the same as the first?