An encryptiondecription system for sending messages consists

An encryption-decription system for sending messages consists of three elements: encode(E), transmit(T), and decode(D) (i.e., this is a series system in E, T, and D). The probability of error is 5%, 10%, and 1% for E, T, and D, respectively. You may assume that for any message, the 3 types of error occur independently. What is the probability that a message:

a. Is completely error-free?

b. Has either an encode error or a decode error?

Solution

(a)

P = (0.95)*(0.90)*(0.99) = 0.84645

(b)

P = (0.95)*(0.01) + (0.05)*(0.99) + (0.05)(0.01) = 0.0595