Imagine a game where someone first rolls a regular fair die, then chooses a specific UNfair coin based on their roll such that the likelihood of flipping a heads on that coin is equal to 1/(die face) (e.g. if a 3 was initially rolled, the likelihood of flipping a heads on the coin selected is 1/3). If a heads is flipped with that coin, then the player gets a piece of chocolate. Please calculate the answers for these problems, and also draw the probability tree with all appropriate labels. You do not need to highlight certain routes identified by the questions, but I'd like to see that you know what the probabilities of each section are and how they are labeled.

a. (7 pts) If you know that the player received a piece of chocolate, what is the likelihood they initially rolled a 6?

b. (7 pts) If you know that the player did NOT receive a piece of chocolate, what is the likelihood they initially rolled an even number on the die?