3. (Competing patterns among coin flips) Suppose that Xn, n 2 1 are i.i.d. random variables with P(X1 = 1) = P(X1 = 0) = 2. (These are just i.i.d. fair coin flips. ) Let A = (a1, a2, a3) = (0, 1, 1), B= (b1, b2, b3) = (0, 0, 1). Let TA = min(n 2 3 : {Xn-2, Xn-1, Xn) = A} be the first time we see the sequence A appear among the Xn random variables, and define TB similarly for B. Find the probability that P(TA