Reconsider the Exercises 11.1.19 and 11.1.20. 

a. Suppose that the rules were changed so that the winner is the first to reach 10 heads or tails, rather than 5. (Continue to assume that the game is interrupted after 3 heads and 2 tails.) How would you expect this rule change to affect the probability that Heather will win the game: larger, smaller, or no change? Explain your reasoning. 

b. Suppose that the rules were changed so that the winner is the first to reach 100 heads or tails, rather than 5 or 10. (Continue to assume that the game is interrupted after 3 heads and 2 tails.) Make an educated guess for the probability that Heather would win the game. Explain your reasoning.

Data from Exercise 11.1.19

Unfinished game: Suppose that Heather and Tom play a game that involves a series of coin flips. They agree that if 5 heads occur before 5 tails do, then Heather wins the game. But if 5 tails occur before 5 heads do, then Tom wins the game. The first five coin tosses result in: H₁, T₂, T₃, H₄, H₅. Unfortunately, the game is interrupted at that point and cannot be finished.