Tossing coins, one fair, one unfair: how to represent the probability tree? Suppose I have a fair coin and an unfair coin. The fair coin has head, tail, the unfair coin has both heads.
You pick one coin at random and toss them two times and observe the outcomes.
Which of the figure below is a better probability tree representation of these experiments (top or bottom)?
I am raising the question because, in the first figure, it seems to draw the head twice is redundant, given that the probability of getting a head is certainty. 


You have to remember that the total possibilities include 4 different sides: the fair coin's heads, the fair coin's tails, the unfair coin's head side A, and the unfair coin's head side B.
When calculating probabilities, you must, of course, consider total possibilities, and that includes the two possible different heads. Just because you can't distinguish between them, doesn't mean they aren't relevant.
Your first tree is the way to go for working out probabilities correctly.
Art of the Problem's Bayes Theorem video explains this exact problem in more detail. For the more general problem of why you should take different sides into account, even when they're the same, read Martin Gardner's "Three Card Swindle" (pp 93-95).
