Question 9
Felicia has a fair six-sided die with four faces numbered $1,2,3,4$ and two blank faces. Nathan has a fair six-sided die numbered 1 to 6. Patrick has a fair twelve-sided die numbered 1 to 12. They take turns in the order Felicia, Nathan, Patrick until someone wins by rolling 1. If Felicia rolls a blank, she keeps rolling until a number appears. Find the probability that Patrick wins.
Use independent rolls of the fair dice. A blank on Felicia’s die does not end her turn.
Use independent rolls of the fair dice. A blank on Felicia’s die does not end her turn.