Ok, I think I'm getting on board, but...

Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.

*Before I flip it*, what's the probability it will turn up heads twice? 25%.

I flip the coin once, and don't tell you what it was. Before I flip the second one, what's the probability it will turn up heads twice? 25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice? 25%.

I turn over one of the coins. It's heads. What's the probability it will turn up heads twice?

...oh.

*OH.**I turn over one of the coins. It's heads. What's the probability ***the other one is heads**? 50%

And if I ask you what were the chances both of them would have come up heads... would you say 25%?