A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day each of the components independently functions with probability p1, whereas on a dry day they independently function with probability p2. The probability of a rainy day is .

(a) (1 points). Give an expression of the probability that the satellite system will function at any given day.

(b) (0.5 points). Evaluate the above probability when n = 3, k = 1, p1 = 0.85, p2 = 0.90, and = 0.20.

(c) (1 points). If the satellite system functioned yesterday what is the probabilty that it was a rainy day? Use n = 3, k = 1, p1 = 0.85, p2 = 0.90, and = 0.20.