These are probabilistic system analysis problems. Please show clear legible work for each one.

2. A diamond network is as defined in Figure 1. The numbers beside each link are the probabilities that that link will be open. Each leg is indepen- dent of the other legs. Calculate the probability that A communicates with Dor Pr[A D]. Figure 1: Diamond Network. L2 - 0.1 L3- 0.3 L4 = 0.2 L5= 0.3 L1= 0.1 3. A computer system is configured as shown using 5 different types of processors. Each is independent of the others. The reliability of P is 95% meaning that it works properly 95% of the time. If P, is 99% reliable, P, is 70% reliable, Pa is 75% reliable, and Ps is 90% reliable, answer the following. (a) What is the overall reliability of the three P3 processors in parallel? (b) What is the overall reliability of the computer system? Figure 2: Computer System. P3 P1 P2 P3 P4 P5 P3 P4