Here's a real twister. I'm not sure if I'm overthinking it?
A fair coin is tossed 6 independent times with the result of 4 heads and 2 tails. What was the most likely number of heads after the first 4 tosses?
Now, I'm not sure if this is a trick question, and the right answer is just 2, or if I need to take into consideration that the probability of a heads in these first 6 tosses is 4 out of 6 - or is it still 1 out of two?