Just for the record, I wasn't trying to save face by changing the question. I didn't change the question at all, I was just asking a different question than my friends were. I acknowledged that the 1 in 50 solution was the correct answer for the question

they were asking, but they could not (or would not) grasp the concept that I was trying to convey.

I'll recreate the situation in dialog using only one friend and a coin flip:

*my friend flips a coin twice, and it lands on heads both times*

Friend: Hey, what are the odds of that?

Me: 1 in 4.

Friend: No, 1 in 2.

Me: Yes, there's a 1 in 2 chance that the coin will land on the same side twice in a row, but only a 1 in 4 chance that it will land on heads twice in a row.

Friend: No, it's always 1 in 2. Go back to school and take a statistics course. Idiot.

(And I realize that this wasn't all made clear initially.* Sorry. But hey, it's sparked some interesting discussion.)

*Edit: Actually, it kind of was (but no worries):

hencethus wrote:One of my friends even used an analogy, saying that by my logic, if he flipped a coin I would have a 1 in 4 chance of guessing correctly on which side it would land.

I tried to explain that while the odds of choosing correctly were 1 in 2, the odds of him flipping heads and me randomly guessing heads specifically was only 1 in 4 (and that the same was true for tails).

Another one of my companions again insisted that I was wrong, and suggested that I go back to school and take a statistics course.