Five-Door Extension to Monty Hall Problem Recall the 5-door version of the Monty Hall problem in which Monty Hall reveals sequentially three doors that are both unchosen and empty. After each revelation, you are given the opportunity to stay or switch.

a) List all the available strategies. Hint/Notation: (stay, stay, stay) is one strategy.

b) Solve for the probability of winning the prize for each of these strategies.