With reference to Exercise 22 of Section 3.5, suppose that the probabilities pi, i =

1, 2,…, are all equal, that is, p1 = p2 = · · · = p.

Let R1(p), R2(p), and R3(p) be the probabilities that electricity passes through the circuits (a), (b), and

(c) of that exercise, respectively.

(i) Draw a graph of Rj(p), j = 1, 2, 3, for 0 ≤ p ≤ 1. What do you observe for Rj(0)

and Rj(1) for j = 1, 2, 3?

(ii) For each j = 1, 2, 3, find the smallest value of p for which

(a) Rj(p) ≥ 0.90;

(b) Rj(p) ≥ 0.95;

(c) Rj(p) ≥ 0.99.