Consider the situation of Example 3-1. Let A_n be the event that the nth trial is successful, B_n be the event that the first success occurred in the nth trial, and A be defined as in Section 3.

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(a) Find P(B) in terms of pn = P(An). (b) Suppose Pn=1 -e-/n. What is the order of the convergence Pn0? What is P(A)? Write an expression for P(Bn). Estimate the order of this probability for large n recalling that -1 - Inn y, where the constant y (called the Euler-Mascheroni constant) approximately equals 0.58. (c) Let pn = 1 -e-1/n. What is the order of the convergence Pn 0? Find P(A)? Find the probability that there will be no successes at all, using the fact that -1/2 = -