Problem 2. Suppose A and B take turns tossing a biased coin which lands heads with probability p. Suppose A tosses first. Find a) the probability that A tosses the first head; b) the probability that B...

Problem 2. Suppose A and B take turns tossing a biased coin which lands heads with probability p. Suppose A tosses first. Find
a) the probability that A tosses the first head;
b) the probability that B tosses the first head. Sketch graphs in terms of p.
c) Suppose that A tosses once, then B twice, then A once, and so on. Repeat parts a) and b) for this scheme, and find the value of p for which A and B have the same probability of tossing the first head.
d) What is B’s chance of tossing the first head for very small values of p? Evaluate this limit as p → 0.